


' THE ARGUMENT 

FOR A FINITIST THEOLOGY 



BY 



RAY HARBAUGH DOTTERER 



A DISSERTATION 

Submitted to the Board of University Studies of the 

Johns Hopkins University in Conformity with the 

Requirements for the Degree of Doctor 

of Philosophy 



PRESS OF 

THE NEW ERA PRINTING COMPANY 

LANCASTER, PA. 

IQI7 



THE ARGUMENT 
FOR A FINITIST THEOLOGY 



BY 

RAY HARBAUGH DOTTERER 



A DISSERTATION 

Submitted to the Board of University Studies of the 

Johns Hopkins University in Conformity with the 

Requirements for the Degree of Doctor 

of Philosophy 



PRESS OF 

THE NEW ERA PRINTING COMPANY 
LANCASTER, PA. 

1917 



.13 T 



Gift 
I 1913 



PEEFACE. 

It was my first intention to take Vaihinger's Philosopliie 
des ALS OB as the subject of my doctoral dissertation; and 
in the spring of 1916 in partial fulfilment of the requirements 
for the Master's degree I did submit an essay on The Philos- 
ophy of the As If in Its Application to Theology. I became 
convinced, however, as the investigation proceeded, that an ex- 
amination of the doctrine of a " finite God " ought to precede 
any attempt to appraise the value of the method of conscious 
illusion. 

I gladly avail myself of the opportunity afforded by a preface 
to acknowledge my indebtedness to Professor A. O. Lovejoy 
for his encouragement and for his patient as well as searching 
and helpful criticism. As I owe much more to his lectures 
and to his oral and written suggestions than to his published 
writings, this general statement may take the place of par- 
ticular acknowledgments and references in detail, which in the 
nature of the case could not often be given. 

E. H. D. 



TABLE OF CONTENTS. 

Chapter Page 

I. Introductory Considerations 1-10 

II. The Monistic Absolute as the Philosophic Equiv- 
alent of God 11-21 

III. The Doctrine of a Finite God 22-31 

IV. Theological Finitisin as the Outcome of a Eational 

Theodicy 32-39 

V. Logical Finitism and the Idea of God 40-49 

VI. Theology and the " New Infinite " 50-70 

VII. Concluding Eeflections on Finitist Theology . . . 71-79 

Bibliography 80-82 



I. 



Introductory Considerations. 

1. The Method of Theological Inquiry. — Theology may 
adopt any one of three methods or it may combine two or all 
of them with varying emphasis npon each. It may appeal to 
the immediate experience of the mystic, or it may simply 
affirm and arrange in systematic form the doctrines authorita- 
tively taught by the Church and the Bible, or it may depend 
upon the "reason" and "conscience" of the individual in- 
quirer. 

The first method would of course be the best if the ex- 
perience in question were not so rare. Assuming that the ex- 
perience of the mystic constitutes a genuine insight into the 
fundamental nature of reality, he nevertheless stands in the 
same relation to his fellowmen as a man with normal vision 
to a race of men blind from their birth. It would be vain for 
the seeing man to discourse of the beautiful colors to be seen 
on every side. Indeed, it would be impossible for him to ex- 
press his experience in words, since language is a social 
product, and the social mpid of the hypothetical race would 
know nothing of color. Thus the mystic's direct vision of God 
can not be described in terms which can be understood by 
ordinary men, and, even from his own point of view or from 
that of a fellow mystic, his experience must ever remain in a 
measure ineffable. Moreover, the difficulty of the mystical 
method is aggravated by the fact that the non-mystic may not 
be willing to grant the objectivity of the mystic's experience. 
And the rarity of his experience may be made a reason for 
regarding it as illusory. Indeed, it may be very plausibly 
maintained that the alleged " revelations " of the traditional 
mystic are evidences of a pathological condition produced by 

1 



2 The Argument for a Finitist Theology. 

his long-continued vigils and fastings. This hypothesis is 
suggested, at least, "by phenomena such as those which Wil- 
liam James has described under the name of the " anaesthetic 
revelation." 1 Accordingly, the non-mystic may be justified 
in believing that his lack of the sense of immediate fellowship 
with absolute reality is not an indication of spiritual poverty, 
but rather an evidence of sanity. 

The second method — that of external authority — received 
a mortal wound in the time of the Reformation, when it was 
discovered that the two sources of authoritative teaching, the 
Church and the Bible, did not always agree. To be sure, the 
Protestant as well as the Roman Catholic still retained the 
method of authority. But the mere knowledge that the 
schism had occurred operated to impair the confidence of the 
intelligent layman in authority of any kind ; and for the theo- 
logically trained man the Protestant appeal to the Bible as 
the only rule of faith and practice contained the seed of its 
own destruction. For the careful study of the sacred writings 
which was logically required by the formal principle of Prot- 
estantism soon showed that these writings, instead of contain- 
ing one uniform and consistent revelation, contain several dif- 
ferent and even conflicting systems of doctrine, and bear clear 
evidence of having been produced in much the same way as 
the other sacred books of antiquity. Thus, although this was 
certainly not the intention of the original Reformers, the log- 
ical and historical result of the Reformation has been to refer 
all questions of doctrine to the "private judgment" of the 
individual Christian. 

The third method, that of reliance upon reason and con- 
science, is, accordingly, the one that is dominant at the present 
time at least among enlightened men and women. Having 
thrown off the authority of the Church, and being distrustful 
of the genuineness of the mystic's experience, they take as 

iThe Will to Believe, pp. 294 ff. (Note: For full titles, etc., see the 
appended bibliography.) 



Introductory Considerations. 3 

their only criterion of truth the reasonableness and ethical at- 
tractiveness of the doctrines in question. 

It is important to note, however, that these three theological 
methods — that of the mystic, that of the authoritarian, and 
that of the self-reliant reasoner — are almost never found pure. 
The traditional mystic has usually been, or at least supposed 
himself to be, a loyal son of the Church ; and his revelations 
have usually been in superficial agreement with its teachings. 
St. Thomas Aquinas employs the method of authority ; but he 
also reasons, so long, at least, as reasoning serves his purpose. 
The "modern" man is no more consistent. Theologians who 
in theory have given up the appeal to any external authority 
nevertheless slip back now and then into the argument from 
Scripture and tradition. And among religious people who are 
not theologians, one result of the modern revolt against the 
authority of the Church and the Book has been a curious sen- 
timentalism in religious thinking, a sort of mitigated mysti- 
cism, which exalts " intuition " and " immediate feeling " as 
over against " reason." 

It must be admitted, I think, that there is a sense in which 
the Scriptures possess authority, and ought to possess au- 
thority, even for the completely emancipated thinker. Their 
authority may be described as suggestive rather than coercive, 
as accidental rather than constitutive. Many biblical doc- 
trines are found to be true, but their truth neither consists in 
nor is established by their quality of being biblical. In other 
words, the authority of the Bible is not like that of a constitu- 
tion or of a legal code, but rather like that of a textbook in 
chemistry or some other laboratory science, the statements 
contained in which are to be accepted or rejected by the stu- 
dent according as they are, or are not, experimentally verified. 

There is also a relative justification for the claims of " in- 
tuition," "instinct," or "immediate feeling." This justifica- 
tion consists in the obvious fact that " reason " in the sense of 
mere intellection is barren. Before there can be any reason- 
ing in this narrow sense of the term, there must be (a) sense- 



4 The Argument for a Finitist Theology. 

perception, and (b) perception of "goods" or of relative 
values. Viewed in this way, reason does not bring forth truth ; 
it has the humbler office of determining which of the offspring 
of " intuition " may be worthy of preservation and ought to be 
acknowledged as true. In other words, we may be said to 
reason when we inquire which of our immediate perceptions 
of fact or of value are implied by or are incompatible with other 
immediate perceptions. Thus there is a sense in which both 
sense-perception and the perception of values are more fun- 
damental than reasoning. But immediate perception alone 
is not a sufficient criterion of truth. For one of our percep- 
tions of fact is that immediate perceptions, whether we limit 
our view to the experience of one mind or consider the ex- 
perience of a larger or smaller group, are not all logically com- 
patible; and that they ought to be logically compatible is one 
of our perceptions of value. If this perception of value is to 
be accepted as genuine, some immediate perceptions and some 
inferences from such perceptions must be rejected as illusory 
or mistaken. But when immediate perceptions are found to 
be mutually repugnant, that is to say, when it is impossible for 
all of them to be genuine in the same logical universe, the 
only arbiter that can decide between them is the reason. In- 
deed this deciding between incompatible verdicts of " intui- 
tion " is what we mean by reason, when we say that the method 
of theology must be the method of reason, rather than of mys- 
tical experience or of dependence upon authority. 2 

2. The Religious Value of the Idea of God. — We value the 
idea of God, and seek to convince ourselves that the idea is 
" real," because we feel the need of God. Our interest, how- 
ever, is practical rather than theoretical. As far as the man 
of science is concerned there may be a God ; but the scientist 
long ago discovered that he, as scientist, has "no need of that 
hypothesis." If, for example, a geologist should tell us that 
the strata of rocks occur in a given order because God laid 
them down in that way, or if a botanist should say that a cer- 

2 Cf. Russell, Scientific Method in Philosophy, pp. 21 f . 



Introductory Considerations. 5 

tain flower has five petals because God made it thus, even the 
least enlightened theist would admit that the assertion is from 
the standpoint of science irrelevant. And, in general, to " ex- 
plain " the occurrence of any particular phenomenon or group 
of phenomena by reference to divine agency is an evasion of 
the problem at issue. 

The value of the idea of God is, then, to be sought in the 
domain of practice rather than of theory. It is moral and 
religious rather than scientific. Traditional theology has 
given the Divine Being the attributes of omnipotence, om- 
niscience, omnipresence, and moral perfection. Modern the- 
ology places moral perfection first, and rightly insists that the 
other attributes have religious value only when moral per- 
fection is presupposed. First of all, God is good ; and his in- 
finite wisdom and might are subservient to his infinite love. 3 

Beginning, then, with the thought of the infinite goodness 
of God, one use of the notion of Deity at once suggests itself. 
God, as the absolutely good being, is man's moral goal or pat- 
tern. "Be ye perfect as your Father in heaven is perfect," 
becomes the maxim of the truly devout worshipper. God is 
the supremely perfect hero, the supreme object of imitation. 

Next, combining the notion of perfect goodness with that of 
omniscience, we derive the idea of God as the righteous and 
completely informed Judge of human conduct. The more 
naive worshipper thinks of a day of judgment at the end of 
the world; the more sophisticated, of a judgment continually 
going on. Whichever way the thought is taken, the believer 
in an all-wise and perfectly good Being has always before him 
the idea of an impartial and all-seeing Spectator who " search- 
eth the reins and the hearts." What is concealed from one's 
fellowmen is fully known to him. Wherein one has been mis- 
judged by his fellows, he is judged rightly by God. At the 
tribunal of the Omniscient One, absolute justice is dispensed. 

Furthermore God is all-powerful. He is the Sovereign of 
the Universe. He has created, and now upholds and governs 

3 Cf . Clarke, The Christian Doctrine of God, pp. 70 ff. 



6 The Argument for a Finitist Theology. 

all. Because he is omnipotent his universal purpose will 
eventually be completely fulfilled. The life of the believer 
himself and that of the group to which he belongs can not 
become a failure. Defeats are merely reverses, suffering is 
chastisement. Faith in an omnipotent God is the ground of 
an assured confidence in the ultimate triumph of the right and 
the eternal survival of the good. 

Lastly, the attribute of omnipresence makes possible the 
thought of a divine Companion and Friend. Though foes 
may scorn and friends forsake, there is a heavenly Father to 
whom one may flee for sympathy. Though the believer is 
alone in the world, he is not alone, for God is with him. 

Such, crudely and inadequately expressed, is the meaning 
of God in the experience of his worshippers. In a word, the 
heart of the true believer is filled with peace — with the " peace 
of God which passeth all understanding." 

But the peace of God is not a peace of quiescence. The truly 
religious man is not simply the contented man. His content- 
ment is combined with a divine discontent with himself and 
his world. A " spark " has disturbed his " clod." He, indeed, 
takes " no thought for the morrow," but he labors for the mor- 
row and for many days thereafter. He seeks " first the king- 
dom of God and his righteousness," and yet is a man of affairs. 
He believes that the sin and the suffering and the sorrow of 
life have their place in the divine economy, yet he is a reformer 
and seeks to make the world better and happier. 

3. Some Antinomies in the Popular Notion of God. — Such 
a paradoxical emotional attitude can hardly be supposed to 
be grounded in a logically consistent doctrine of God. Indeed 
the paradoxical character of the typical religious experience 
would suggest a self-contradictory ground. And no very 
profound study is required to show that the popular notion 
of God is shot through with contradictions. Some of these 
are evident to the popular mind itself; others do not appear 
until the notion is examined with more than ordinary care. 



Introductory Considerations. 7 

A few of the more obvious of these difficulties are the fol- 
lowing. 

(a) Goodness versus Power in Relation to the Existence of 
Evil. — According to traditional theology the world is partly 
evil, and is nevertheless the work of Infinite Power and Per- 
fect Goodness. The antinomy is obvious: How can Omnip- 
otent Goodness be supposed to have produced or to be the 
ground of an imperfect world? Attempts at reconciliation 
merely repeat the difficulty in a new form. Thus we hear 
men say that if God had not permitted some particular evil a 
greater evil would have occurred; that the pains and suf- 
ferings of life are means of chastisement and moral purifica- 
tion; that sin makes possible forms of goodness which out- 
weigh both the sin itself and the evil consequences resulting 
from it. But it is obvious that this mode of explanation itself 
presupposes some limitation of divine power. It assumes that 
evil is a necessary condition of the perfection of the world, 
and that even Omnipotence is bound by this condition. The 
existence of evil is a proof of God's inability to remove it 
from his world, or, what amounts to the same thing, of his 
inability to remove or prevent it without defeating his uni- 
versal purpose. Again, if we adopt the evolutionary point of 
view, and admit the idea of a temporal process into our rea- 
sonings about good and evil, we may say that, while God's 
world is not yet perfect, its perfection will come at the end of 
the evolutionary process. But the idea of evolution, the very 
notion of a process, is irreconcilable with omnipotence. For 
the idea of a process implies hindrance or retardation, and 
therefore the finitude of the energizing agent. 

(b) Righteousness versus Predestination. — This is a special 
and aggravated case of the preceding difficulty. If God is 
omnipotent, he is the absolute Sovereign of his world, and all 
events are in accordance with his will; but if all events, in- 
cluding human actions, bad as well as good, are willed by 
God, then God is the real author of human sin. 



8 The Argument for a Finitist Theology. 

(c) The Hearing of Prayer versus Omniscience. — If God 
be thought of after the analogy of an ancient oriental monarch, 
prayer may be regarded as necessary in order to propitiate the 
Despot when he is angry, or to overcome his carelessness, or 
his indifference to the well-being of his subjects. But, surely, 
in the case of a Sovereign who is perfectly good, prayer is not 
needed for this purpose. Again if God's power be limited, it 
may be maintained with considerable plausibility that prayer 
is a means of supplementing the energy which is insufficient 
for the accomplishment of some good purpose. But, according 
to the traditional doctrine, there is no defect of power, and 
prayer can not be justified in this way. Once more, if God's 
knowledge were limited, prayer, in the sense of petition for 
some definite boon, might be regarded as a means of inform- 
ing God concerning human needs. The analogy of the eastern 
monarch here recurs, and doubtless has figured largely in the 
common theory of prayer. But if God is omniscient, we can- 
not tell him anything, and the antinomy remains unsolved. 

(d) Personality versus Immutability. — According to tra- 
ditional religious thought, God is a person, a Friend or Father 
with whom men may enjoy fellowship. On the other hand, 
he is also said to be "eternal," not merely in the sense that 
his existence is without beginning or end, but in the sense 
that he is supertemporal and immutable. But the attributes 
of personality and immutability are plainly contradictory. 
For a person is the subject of experience, and experience im- 
plies time. At any rate, human persons are in time; succes- 
sion is of the very essence of their life ; and therefore a divine 
Person who is assumed in any meaningful sense to know them 
and to fellowship with them must also be in time. 

4. A Prospectus of the Ensuing Discussion. — We have seen 
that the attempt to think of God as omnipotent, omniscient, 
and immutable, and at the same time as a personal Being who 
is perfectly good, and who enters into communion with men 
and may be influenced by their petitions, is logically impos- 
sible. Accordingly, the next three sections will be devoted to 



Introductory Considerations. 9 

a critical exposition of two rival attempts to rationalize or to 
find a substitute for the traditional (Christian) conception of 
Deity. These contrasted theories are the theory of monistic 
idealism, which in its specifically theological aspect is a theory 
of the divine immanence, and that of pluralism, with its doc- 
trine of a " finite " God. As my examination of these rival 
theories leads me to the acceptance of the latter, I have called 
the whole discussion " an argument for a finitist theology." 

God has been said to be in-finite in two different senses : (1) 
He has been said to be the Whole of reality, or at least to be 
the Ground and Source of all that is. (2) He has been said 
to be infinite in the literal numerical sense of the word; for 
example, to know an infinite multiplicity of knowledge-ele- 
ments, or to be " eternal,' 7 either in the sense of living through 
an infinite sequence of moments, or in the sense of being super- 
temporal and yet in some manner containing infinite time. 
The God of monistic idealism, for example the "Absolute" 
as described by Josiah Royce, is held to be infinite in both of 
these senses. The Absolute is the all-inclusive Reality; and, 
by virtue of Royce's fundamental epistemological presupposi- 
tions, his one eternal or timeless Purpose includes or implies 
an infinite multiplicity of elements. Over against this monis- 
tic theory stand the theory of John Stuart Mill and William 
James, on the one hand, and that of Charles Renouvier. on the 
other. These theories, which I shall call respectively " ethical 
finitism" and "logical finitism," are mutually compatible, 
but, as we shall see, do not necessarily imply one another. 
The doctrine of a " finite " God as it is expounded by Mill 
and James consists essentially in the denial of God's infinitude 
in the former of our two senses. According to this view, God 
is not omnipotent. It is a view which is founded chiefly upon 
the difficulties of theodicy, upon the impossibility of " justify- 
ing the ways of God to man," if God is assumed to be infinite 
in the sense of possessing all knowledge and all power. Ac- 
cording to Renouvier and his school, the finitude of the world 
and of God logically results from the self-contradiction which 
lurks in the conception of a " realized infinite." 



10 The Argument for a Finitist Theology. 

The discussion of the theories of Royce and Renouvier will 
lead us to an examination of the so-called New Infinite of re- 
cent mathematics, as it has been .defined by Richard Dede- 
kind and Georg Cantor; for by his own account the idealism 
of Royce is logically dependent upon the validity of this con- 
ception, and the entire Renouvierist philosophy must go by 
the board if, as is maintained, the formulation of this new 
definition of infinity frees the notion of a realized infinite 
from the difficulties which Renouvier found in it. In view, 
therefore, of the strategic importance of this subsidiary issue, 
I shall devote Section VI to an examination of these con- 
trasted ways of thinking about the infinite. My conclusion 
will be that the formulation of the " new " infinite has not re- 
moved the logical objections to monistic idealism, nor at all 
impaired the cogency of the reasonings of Renouvier and his 
disciples. 

The last section will contain a brief summary of all that 
has gone before, together with a further examination of the 
conception of a " finite " God. 



II. 



The Monistic Absolute as the Philosophic Equivalent 

of God. 

In our attempt to find a conception of God that is both 
rationally satisfactory and religiously serviceable we turn to 
the philosophers. Two types of theory may be distinguished : 
the monistic and the pluralistic. According to the monistic 
theories, God is the whole of existence; pluralistic theories, 
on the other hand, make God the part, but the controlling part 
of existence. 

1. Monistic Idealism as a Fulfilment of Traditional The- 
ology, — In this chapter we shall consider the monistic revision 
of the traditional conception of God. The theory of Josiah 
Royce may be taken as a typical expression of this class of 
theories. 4 

Royce's conception of God is regarded by its author, "not 
as destroying, but as fulfilling, the large collection of slowly 
evolving notions that have appeared in the course of history in 
connection with the name of God." 5 He insists that "what 
the faith of our fathers has genuinely meant by God is, despite 
all the blindness and all the unessential accidents of religious 
tradition, identical with the inevitable outcome of a reflective 
philosophy." 6 This conception "undertakes to be distinctly 
theistic, and not pantheistic. It is not the conception of an 
Unconscious Reality, into which finite beings are absorbed; 
nor of a Universal Substance, in whose law our ethical inde- 
pendence is lost; nor of an Ineffable Mystery, which we can 
only silently adore. On the contrary, every ethical predicate 

*For Royce's account of his philosophic ancestry, see The 'Religious 
Aspect of Philosophy, pp. ix ff. 

6 Royce, et ah, The Conception of God, p. 48. 

6 Ibid., p. 50; see also The Problem of Christianity, Preface. 

11 



12 The Argument for a Finitist Theology. 

that the highest religious faith of the past has attributed to 
God is capable of exact interpretation in terms of our present 
view." 7 

Professor Royce's contribution to the theistic discussion con- 
sists, then, in the identification of God with the Absolute of 
idealistic philosophy; and in attempting so to define the Ab- 
solute as, on the one hand, to avoid the self-contradictions 
which are to be found in the notion of Deity as ordinarily con- 
ceived, and, on the other hand, to enrich the notion of the Ab- 
solute so that it shall be a fit object for the religious emotions 
or attitudes of awe and reverence, of faith, loyalty, and love. 
It is important to remember, however, that many idealistic 
philosophers have not been willing to regard the Absolute as 
personal, or in any significant sense as a Self. Thus Mr. P. 
H. Bradley does not apply the name God to the Absolute, 8 
and, if Dr. McTaggart is right, Hegel himself, who is com- 
monly regarded as the father of this general way of thinking, 
ought not to have done so. 9 His use of " God " and of other 
religious terms, says McTaggart, was merely an accommoda- 
tion to the " current mythology " of the time. According to 
Professor Royce, however, the Absolute of monistic idealism 
is what the Church has really meant all along by God; but 
this meaning has been only vaguely apprehended, and there- 
fore only imperfectly expressed. 

As defined by Royce, God, or the Absolute, includes in his 
own consciousness and will the content of all finite minds. 
The individual self is an identical part of the Divine Self. 10 

" Let us sum up, in a few words," says Royce, " our whole 

argument. There is, for us as we are, experience. Our 

thought undertakes the interpretation of this experience. 

Every intelligent interpretation of an experience involves, 

however, the appeal from this experienced fragment to some 

7 Ibid., p. 49. 

s Appearance and Beality, pp. 446 ff. 

o Studies in Hegelian Cosmology, pp. 59 ff., 213. 

io The Conception of God, p. xiii ; Hibbert Journal, I, 44. 



The Monistic Absolute. 13 

more organized whole of experience in whose "unity this frag- 
ment is conceived as finding its organic place." 1 x " There 
must be an experience to which is present the . . . actual 
limitation and narrowness of all finite experience." 12 

Furthermore, since every reality exists "just in so far as 
there is experience of its existence," 13 since, in other words, 
everything that is, is the content of mind, it follows that the 
"things" which we ordinarily think of as non-mental are in- 
eluded in the content of the Absolute Self. 

" The reality that we seek to know," says Royce, " has al- 
ways to be defined as that which either is or would be present 
to a sort of experience which we ideally define as an organized 
— that is, a united and transparently reasonable experience. 
We have, in point of fact, no conception of reality capable of 
definition except this one." 14 " To assert that there is any 
absolutely real fact indicated by our experience, is to regard 
this reality as presented to an absolutely organized experience, 
in which every fragment finds its place." 15 

Professor Royce's conception of the Absolute is attained,' 
then, by combining the traditional attribute of omniscience 
with the idealistic presupposition that to be is to be known as 
being. It may be remarked in passing that if this presuppo- 
sition is denied, the whole edifice of monistic idealism falls to 
the ground. We are not now concerned, however, with the 
question of the existence of the Absolute, but only with its 
definition. If the presupposition is granted, it is evident that, 
as Royce maintains, "In order to have the attribute of Om- 
niscience, a being would necessarily be conceived as essen- 
tially world-possessing." 16 

The error and suffering and sin of our finite lives are all 
due to the fragment ariness of our experiences. When taken 

11 The Conception of God, p. 42. 

12 Ibid., p. 41. Cf . The Religious Aspect of Philosophy, p. 441. 
is The Conception of God, p. 43. 

i* Ibid., p. 30. 
is Ibid., p. 42. 
Mlbid., p. 13. 



14 The Argument for a Finitist Theology. 

up into the infinite completeness of the Universal Self, all the 
imperfections of existence cancel out, or better, all are re- 
quired to constitute the perfection of the Whole. We, as frag- 
ments of the Absolute, may be victims of misfortune, unhappy, 
discontented, sinful. But the Absolute is perfectly good. Our 
imperfection, and our thought of the world as imperfect, are 
the consequence of the limitation of our knowledge. We know 
in part; the Absolute knows the Whole, and pronounces it 
complete, and perfectly good. 17 

" Misfortune comes to us, and we ask : What means this hor- 
ror of my fragmentary experience ? — why did this happen to 
me ? The question involves the idea of an experience that, if 
present, would answer the question. Now such an experience, 
if it were present to us, would be an experience of a certain 
passing through pain to peace, ... of a certain far more ex- 
ceeding weight of glory that would give even this fragmentary 
horror its place in an experience of triumph and of self-pos- 
session. In brief, every time we are weak, downcast, horror- 
stricken, alone with our sin, the victims of evil fortune or of 
our own baseness, we stand, as we all know, not only in pres- 
ence of agonizing fragmentary experiences, but in presence of 
besetting problems, which in fact constitute the very heart of 
our calamity. . . . Well, then, if the divorce of idea and ex- 
perience characterizes every form of human consciousness of 
finitude, of weakness, of evil, of sin, of despair, you see that 
Omniscience, involving, by definition, the complete and final 
fulfilment of idea in experience, the unity of thought and act, 
the illumination of feeling by comprehension, would be an 
attribute implying, for the being who possessed it, much more 
than a universally clear but absolutely passionless insight. An 
Omniscient Being could answer your bitter Why? when you 
mourn, with an experience that would not simply ignore your 
passion. For your passion, too, is a fact. It is experienced. 
The experience of the Omniscient Being would include it. 

17 The Religious Aspect of Philosophy, pp. 444 and 449; Sources of Be- 
ligious Insight, p. 224. 



The Monistic Absolute. 15 

Only his insight, unlike yours, would comprehend it, and so 
would answer whatever is rational about your present ques- 
tion. ... In order to have the attribute of omniscience, a 
being would necessarily ... be conceived as omnipotent, and 
also as in possession of just such experience as ideally ought 
to be; in other words, as good and perfect." 18 

2. Some Difficulties of Monistic Idealism. — As has already 
been remarked, Professor Koyce's proof that there is such an 
Absolute Being as he has defined, rests upon the presupposition 
that all being is being known, that all existence is mental. 
Unless this assumption be granted, the argument goes to 
pieces. Moreover, in Chapter V we shall meet a consideration, 
which will make it impossible for us to conceive that the Ab- 
solute Self is real. This is the self-contradiction involved in 
the notion of a " realized infinite." For the present, however, 
I shall limit myself to pointing out certain other difficulties, 
which, it seems to me, are inseparable from the conception of 
the Absolute as it is defined by Eoyce. 

(a) The first of these may be called the religious difficulty. 
We may approach it by considering a conception near akin 
to that of the monistic Absolute, namely, the conception of 
God as immanent in his world. If God is thought of as 
transcendent, and the supernatural and the natural regarded 
as mutually exclusive categories, then the friend of religion 
must view the progress of science with alarm. A division of 
the world between science and religion, between Nature and 
God, might be reasonably satisfactory, if one could be sure 
that the boundary would remain permanently fixed. But, if 
we define the natural as that which is explicable in terms of 
scientific law, then, as science extends its territory, and pro- 
claims its belief in the possibility of a universal conquest, the 
outlook for religion becomes dark indeed. If the supernatural 
is defined as that which is not natural, the scientific view of 
the world leaves no place for God. 

In this perilous situation "liberal" theologians have em- 

is The Conception of God, pp. 11 ff. 



16 The Argument for a Finitist Theology. 

phasized the immanence of God, and have said that all events 
are supernatural, since all are produced by, or are particular 
expressions of, the immanent God. The difficulty of this pro- 
cedure is, however, that, in thus preserving the right to use 
the word God, we are in danger of so impoverishing the idea 
of God that it becomes of little value as a religious conception. 
In order to meet this peril it is then necessary to insist that 
God is transcendent as well as immanent. Thus to avoid the 
danger of pantheism, Dr. William Newton Clarke, for ex- 
ample, maintains that " Transcendence is first. ... It is the 
transcendence that gives the immanence its meaning. . . . 
The Christian thought of God is not so much that the im- 
manent God is transcendent, as it is that the transcendent God 
is immanent." 19 The God who is immanent is the Personal 
God. 

The difficulty, however, is to see how a completely immanent 
God can be personal. Merely to say that God is immanent, 
and that therefore all events are acts of God, and that for this 
reason the theist need not be troubled by the claim of science 
to include all events in its realm ; and also to say that God is 
transcendent and personal as well as immanent, does not solve 
the difficulty ; any more than to say that a certain geometrical 
figure is round and also has four right angles will remove the 
self-contradiction from the notion of a square circle. In the 
same way, for Koyce merely to say that the Absolute is Per- 
sonal, and that his theory is a theism and not a pantheism does 
not suffice. Unless we assume that completeness, as opposed 
to fragmentariness, is per se worthy of reverence, an assump- 
tion which is by no means self-evident, there seems to be no 
sufficient reason for worshipping the Absolute ; 20 and it seems 
impossible for us to enter into fellowship with such an entity, 
unless we consciously or unconsciously think of it as if it 
were a Person distinct from, and standing over against us and 
all others. 

is The Christian Doctrine of God, p. 322. 

20 See Professor Mezes's criticism of Eoyce's Ultimate Being, The Con- 
ception of God, pp. 54 ff. 



The Monistic Absolute. 17 

(b) Furthermore, there are certain psychological difficul- 
ties in the conception of the Absolute. These result from the 
circumstance that some of our experiences, which are by def- 
inition experiences of the Absolute also, are conditioned by 
our very finiteness, and therefore can not be experienced by 
an Absolute being. Such experiences are hope and fear, for 
example. A being who knows perfectly what the morrow will 
bring forth can not hope for anything on the morrow ; neither 
can he fear. If I am sure of obtaining a certain boon, I do 
not hope to obtain it ; still less can I be said to fear lest I shall 
not obtain it. Both of these emotions presuppose some degree 
of uncertainty with reference to the future, and such uncer- 
tainty is incompatible with omniscience. In the same way it 
is impossible that an omniscient being should ever experience 
curiosity or the joy of discovery. The Absolute, too, must be 
without the experience of sin and repentance. Yet, as Abso- 
lute, he must contain all these experiences. 

If all we mean when we say that a being is omniscient is 
that he hnows about all the experiences of all other beings (in 
addition to all the other knowledge that he is assumed to pos- 
sess), then these difficulties do not arise. The Absolute may 
well enough be assumed to know all about my states of mind ; 
but he cannot without contradiction be assumed to include in 
the totality of his experience the identical hopes and fears and 
feelings of repentance that I feel. 

The same remark must be made of our experience of tem- 
poral succession. God, or the Absolute, is said to know all in 
an Eternal Now. 21 But if that is the nature of his knowledge, 
it is impossible that He should know things in succession. It 
must be admitted, however, that both kinds of knowledge are 
attributed to him. It is common to make a distinction be- 
tween a holy place in which a real experience of succession is 
found, and a Holy of Holies in which all " bondage to succes- 
sion " is overcome. Thus the late Professor Bowne, although 

21 The Beligious Aspect of Philosophy, p. 441 ; The Conception of God, 
pp. 59 f.; The World and the Individual, II, 138 ff. 



18 The Argument for a Finitist Theology. 

he criticizes the absolute idealism of the Hegelian school on 
the ground that " such a system excludes all movement and 
progress, and the appearance of movement can only be reck- 
oned a delusion," insists nevertheless that a from the theistic 
standpoint the infinite must be viewed as possessing an eternal 
mind so far as itself is concerned." On the other hand, " the 
infinite must be in time, so far as the world process is con- 
cerned." 22 

Dr. William Newton Clarke writes in a similar strain: 
" Succession is essential to the significance of events in time, 
and if God had no knowledge of it he could not understand 
events or the history that is composed of them, or the life of 
his children. He has both kinds of knowledge. He eternally 
knows all things at once, and is also aware of them as they 
become realized in time and space; and in the perfect mind 
there is no inconsistency between these two modes." 23 

But does this last clause mean anything more than that con- 
tradictions may be tolerated in the case of affirmations con- 
cerning the perfect mind, which would be intolerable if the 
mind were not perfect? And why this reluctance to subject 
the perfect mind to the " bondage of succession " ? We may 
say, if we will, that God would be limited by succession; but 
is he not limited in just the same sense by the law of contra- 
diction and the law of love ? The attempt to affirm the reality 
of both kinds of knowledge in the Divine mind suggests, once 
more, the attempt to define a plane figure that is both square 
and circular. 

This view can be logically defended in no other way than 
by a denial of the reality of the experience of time. Says Pro- 
fessor Mezes, interpreting the view of Royce, " Speaking tech- 
nically, time is no reality ; things seem past and future, and in 
a sense, non-existent to us, but in fact they are just as gen- 
uinely real as the present is. Is Julius Csesar dead and turned 
to clay ? ISTo doubt he is. But in reality he is also alive, he 

22 Metaphysics, pp. 486, 240 f. 

23 The Christian Doctrine of God, p. 346. Cf. pp. 295 ff. 



The Monistic Absolute. 19 

is conquering Spain, Gaul, Greece, Egypt. He is leading the 
Roman legions into Britain, and dominating the envious Sen- 
ate, just as truly as he is dead and turned to clay — just as truly 
as you now hear the words I am speaking. Every reality is 
eternally real; pastness and futurity are merely illusions." 24 

But if the experience of succession is illusory, what then is 
real? The fact that of two experiences one comes after the 
other is certainly as real as anything can be. If the two ex- 
periences are cognitive, it may indeed happen that the events 
to which they refer really occurred in a different order from 
that in which I have experienced them; or these events may 
really have been simultaneous; but the experiencings them- 
selves are in the order in which they come, and it is meaning- 
less to say that they are really in a different order, or that 
they are simultaneous. If the Absolute were merely supposed 
to know about them, he might have knowledge of them both at 
the same moment, although I experience them one after the 
other ; but if my experiencings are numerically the same as cer- 
tain experiencings of His, then the order in which they occur 
for me must also be the order in which they occur for Him. 

(c) Last and most important of all are the ethical diffi- 
culties of the conception of the Absolute. If all thoughts are 
thoughts of God, and all events are acts of God, then our evil 
desires and purposes are purposes and desires of God, and all 
our sinful deeds are deeds of God. The antinomy between 
predestination and the goodness of God, which has troubled 
traditional and popular theology, thus appears in an aggra- 
vated form in the theology of immanence. The logical conse- 
quence is a denial of the genuineness of the distinction between 
good and evil, right and wrong. If the Absolute must be con- 
ceived to be " in possession of just such experience as ideally 
ought to be," 25 then, from the standpoint of the Absolute, there 
is no reason for wishing that anything should be other than it 

2* Eoyce, et ah, The Conception of God, p. 60. 

25 The Conception of God, p. 13. 

26 The Religious Aspect of Philosophy, pp. 454 f . ; Sources of Religious 
Insight, pp. 237, 224. 



20 The Argument for a Finitist Theology. 

is ; no reason for pronouncing one thing evil and another good. 

The fact that the partisans of the monistic Absolute, like 
believers in the Calvinistic doctrine of predestination, have 
been zealous in good works, and have been strenuous advo- 
cates of reform and good haters of iniquity of all sorts, does 
not alter the fact that the logical consequence of their creed is 
a life of resignation and acquiescence. If the account which 
monistic idealism gives of the world is true, not only is it 
logically right for me to endure my private pains and disap- 
pointments without grumbling, and to " spiritualize " and 
"idealize" them, seeing that the Absolute is not unhappy, 
and the Absolute is not disappointed, and that in spite of 
these "partial evils" "in the universe as a whole the good 
triumphs " ; 26 but there is no reason why I should bestir 
myself to lighten the sorrows of my fellow men, since their 
sorrows too, just as they are, have their proper place in the 
eternal felicity of the Absolute and contribute to the perfec- 
tion of the whole. 

It may perhaps be said that, since nothing that we can do can 
disturb or impair the eternal perfection of the Absolute, we 
may still, without lack of logical consistency, and without de- 
fect of loyalty to the good of the Whole, attempt to brighten 
the little corner in which we are placed. But if the present 
proportion of light and shadow is just the correct one to 
produce the perfection of the Whole, then, assuming the 
Whole to remain perfect, in brightening one corner, I should 
automatically darken some other corner; and there is no suf- 
ficient reason for wishing to do that. If, on the other hand, 
it should be said that the precise proportion of light and shade 
in the universe is a matter of indifference, and that conse- 
quently I can seek my own happiness and that of others with- 
out necessarily diminishing the felicity of the Absolute or of 
any sentient being, then we should have to conclude that the 
doctrine of the Absolute is without any moral significance 
whatever; for, if my pains and sorrows are not necessary to 
the felicity of the Absolute, the doctrine of the Absolute pro- 
vides no reason why I should bear them patiently. 



The Monistic Absolute. 21 

The monistic idealist is sure to object at this point that the 
argument of the last few paragraphs is based upon an inade- 
quate account of Royce's ethical theory. For Professor Royce 
speaks not only of evils which are to be endured, but also, and 
much more, of evils which are to be overcome; and, in his 
theory, the typical evil is not physical pain, or mere pain of 
any kind, but rather the bad will of a moral agent. 

This objection of the monistic idealist, however, introduces 
considerations which had better be postponed until we have 
given an account of the ethical argument for theological 
finitism. 



III. 

The Doctrine of a Finite God. 

The monistic theories make a grudging admission of the 
individual and particular facts of life. The pluralistic 
theories, on the other hand, emphasize these facts and take 
their departure from them. For the pluralistic theories the 
particular and the individual constitute the true reality. The 
dirt and grime of actual experience must not be forgotten or 
ignored in the thought of an Eternal Reality which is sup- 
posed, in some mysterious or very imperfectly understood 
manner, to be perfect, though including imperfection. Sin 
and suffering are not illusions which are overcome in an 
Eternal ]STow, or fragmentary experiences which together form 
the perfect Whole of existence. On the contrary, the victory 
of the Good is not yet achieved ; the world is not completed ; 
the process of evolution is a reality. God is not all-powerful ; 
but he is a Struggler, who is hindered and thwarted, at least 
for the time being, by necessities which are beyond his con- 
trol. The time process is required for the accomplishment of 
his good purposes. 

In other words, by those who hold the pluralistic view of 
the world, the tradition that God is Absolute, Infinite, Om- 
nipotent, Omniscient, Immutable, etc., is definitely and con- 
sciously abandoned; and, if the belief in God is retained, he 
is thought of as a finite being, one among many, yet supreme 
above all. 

This, in broad outline, is the doctrine of God expounded by 

John Stuart Mill, William James, and other philosophical 

radicals. 27 They were not afraid of unorthodox phraseology, 

27 For more recent expositions of the finitist doctrine, see H. G. Wells, 
God the Invisible King, and E. H. Eeeman, Bo We Need A New Idea of 
God? 

22 



The Doctrine of a Finite God. 23 

they were not much influenced by the mere form and sound 
of words. Most theological and religious writers, on the other 
hand, and many philosophers, manifest a curious reverence for 
words and phrases that have been hallowed by long use and a 
corresponding reluctance to accept new forms of expression. 
They are, accordingly, disposed to shy at such a word as finite 
when it is employed as an adjective modifying the term God; 
and yet many of them are not in principle so far as they seem 
from the view suggested by the phrase formed of these two 
words. Thus many monistic idealists have held that suffering 
must be a genuine experience of the Absolute; and it has 
become a commonplace of moral and religious exhortation to 
say that we are co-workers with the Omnipotent. We may 
question the logical consistency of Absolutist philosophers and 
religious exhorters, and yet rejoice that, even in opposition to 
the logical implications of their systems, they have sought to 
be loyal to the facts of human experience. 

In the fifth chapter we shall consider the arguments of those 
who have arrived at a finitist theology by a logical analysis of 
the notion of the realized infinite. These thinkers have come 
to the conclusion that it is impossible without logical incon- 
sistency to say that anything that is, is infinite. Therefore 
neither God nor the world can be said, if we speak strictly, to 
be infinite. In this and the immediately following chapter, 
we shall restrict our attention to what may be called the ethical 
argument for the doctrine that God is finite. 

This argument is essentially a theodicy, an attempt to jus- 
tify the ways of God to men in view of the manifest evil and 
imperfection of the world. In brief, the argument is this: 
God can not be thought to be at once omnipotent and perfectly 
good. If we say that he is omnipotent, that his sovereignty is 
complete, that all events that occur are willed by him ; then it 
follows that he is responsible for the actual world, which is 
partly evil, and, accordingly, that he is not perfectly good. 
If we begin at the other end, and say that God is perfectly 
good, then we must deny that he is omnipotent. 



24 The Argument for a Finitist Theology. 

John Stuart Mill may be taken as a representative of this 
general tendency. His argument rests upon the evident 
cruelty and recklessness of Nature, from which he infers the 
limited power of the Author of Nature. " Next to the great- 
ness of these cosmic forces, the quality which most forcibly 
strikes everyone who does not avert his eyes from it, is their 
perfect and absolute recklessness. They go straight to their 
end, without regarding what or whom they crush on the road. 
... In sober truth, nearly all the things which men are 
hanged or imprisoned for doing to one another, are nature's 
everyday performances. Killing, the most criminal act recog- 
nized by human laws, Nature does once to every being that 
lives. . . . Nature impales men, breaks them as if on the 
wheel, casts them to be devoured by wild beasts, burns them 
to death, crushes them with stones like the first Christian 
martyr, starves them with hunger, freezes them with cold, 
poisons them by the quick or slow venom of her exhalations, 
and has hundreds of other hideous deaths in reserve, such as 
the ingenious cruelty of a Nabis or a Domitian never sur- 
passed. All this, Nature does with the most supercilious dis- 
regard of mercy and of justice. . . . Next to taking life is 
taking the means by which we live ; and Nature does this, too, 
on the largest scale and with the most callous indifference. A 
single hurricane destroys the hopes of a season; a flight of 
locusts, or an inundation, desolates a district ; a trifling chem- 
ical change in an edible root, starves a million of people. . . . 
Everything in short, which the worst men commit either 
against life or property is perpetrated on a larger scale by 
natural agents. . . . All which people are accustomed to 
deprecate as l disorder ' and its consequences, is precisely a 
counterpart of Nature's ways. Anarchy and the Reign of 
Terror are overmatched in injustice, ruin, and death, by a hur- 
ricane and a pestilence." 28 

The main thesis of the Essay on Nature is that it is " irra- 
tional and immoral" to "make the spontaneous course of 
28 Three Essays on Religion, pp. 28 ff. 



The Doctrine of a Finite God. 25 

things the model" of man's voluntary actions. 29 The inci- 
dental conclusion of the essay is the position which has been 
stated by way of anticipation, namely, that it is absurd and 
irrational to hold that God is perfectly good and also all- 
powerful. " The only admissible moral theory of Creation," 
says Mill, " is that the Principle of Good cannot at once and 
altogether subdue the powers of evil, either physical or moral. 
. . . Those who have been strengthened in goodness by rely- 
ing on the sympathizing power of a powerful and good Gov- 
ernor of the world, have, I am satisfied, never really believed 
that Governor to be, in the strict sense of the term, omnip- 
otent. They have always saved his goodness at the expense 
of his power." 30 Eecurring to the same thought in the essay 
on the Utility of Religion, Mill contends that " one only form 
of belief in the supernatural — one only theory respecting the 
origin and government of the universe — stands wholly clear 
both of intellectual contradiction and of moral obliquity. It 
is that which, resigning irrevocably the idea of an omnipotent 
creator, regards Nature and Life not as the expression through- 
out of the moral character and purpose of the Deity, but as 
the product of a struggle between contriving goodness and an 
intractable material, as was believed by Plato, or a principle 
of evil, as was the doctrine of the Manichseans." 31 

Mill shows that all the attempts that are made to escape 
this conclusion are futile, and tacitly presuppose it. " That 
much applauded class of authors, the writers on natural the- 
ology, . . . have exhausted the resources of sophistry to make 
it appear that all the suffering in the world exists to prevent 
greater — that misery exists, for fear lest there should be 
misery : a thesis which, if ever so well maintained, could only 
avail to explain and justify the works of limited beings, com- 
pelled to labor under conditions independent of their own will ; 
but can have no application to a Creator assumed to be om- 

2» IUd., p. 64. 
30 IUd., pp. 39 f . 
si Ibid., p. 116. 



26 The Argument for a Finitist Theology. 

inpotent, who, if he bends to a supposed necessity, himself 
makes the necessity which he bends to. If the maker of the 
world can all that he will, he wills misery, and there is no 
escape from the conclusion." 

If we nevertheless attempt to escape by saying that "the 
goodness of God does not consist in willing the happiness of 
his creatures, but their virtue," Mill replies that " if the 
Creator of mankind willed that they should all be virtuous, 
his designs are as completely baffled as if he had willed that 
they should all be happy." 32 

"But, it is said, all these things are for wise and good 
ends." It may be said that "we do not know what wise 
reasons the Omniscient may have had for leaving undone 
things which he had the power to do. It is not perceived that 
this plea itself implies a limit to Omnipotence. When a thing 
is obviously good and obviously in accordance with what all 
the evidences of creation imply to have been the Creator's de- 
sign, and we say we do not know what good reason he may 
have had for not doing it, we mean that we do not know to 
what other, still better object — to what object still more com- 
pletely in the line of his purposes, he may have seen fit to post- 
pone it. But the necessity of postponing one thing to another 
belongs only to limited power. Omnipotence could have made 
the objects compatible. Omnipotence does not need to weigh 
one consideration against another. . . . No one purpose im- 
poses necessary limitations on another in the case of a Being 
not restricted by conditions of possibility." 33 

Therefore "the notion of a providential government by an 
omnipotent Being for the good of his creatures must be en- 
tirely dismissed." 34 If we believe that God is all-powerful 
and that Nature is his handiwork, our " worship must either 
be greatly overclouded by doubt, and occasionally quite dark- 
ened by it, or the moral sentiments must sink to the low level 
of the ordinances of Nature: the worshipper must learn to 

32 iud., p. 37. 

33 Hid., pp. 179 f . 

34 iud., p. 243. 



The Doctrine of a Finite God. 27 

think blind partiality, atrocious cruelty, and reckless injustice, 
not blemishes in an object of worship, since all these abound to 
excess in the commonest phenomena of Nature. . . . He who 
comes out with least moral damage from this embarrassment, 
is probably the one who . . . confesses to himself that the 
purposes of Providence are mysterious, that its ways are not 
our ways, that its justice and goodness are not the justice and 
goodness which we can conceive and which it befits us to prac- 
tise. When, however, this is the feeling of the believer, the 
worship of the Deity ceases to be the adoration of abstract 
moral perfection. It becomes the bowing down to a gigantic 
image of something not fit for us to imitate. It is the worship 
of power only." 35 

The very argument which has been chiefly relied upon to 
prove the existence of God, namely, the argument from design, 
far from establishing his omnipotence, is easily shown to be 
incompatible with it. " It is not too much to say that every 
indication of Design in the Kosmos is so much evidence 
against the Omnipotence of the Designer. For what is meant 
by Design ? Contrivance : the adaptation of means to an end. 
But the necessity of contrivance — the need of employing means 
— is a consequence of the limitation of power. . . . Wisdom 
and contrivance are shown in overcoming difficulties, and there 
is no room for them in a Being for whom no difficulties exist. 
The evidences, therefore, of Natural Theology distinctly im- 
ply that the author of the Kosmos worked under limitations ; 
that he was obliged to adapt himself to conditions independent 
of his will, and to attain his ends by such arrangements as 
those conditions admitted of." 36 

A creed like this makes human life significant. "A vir- 
tuous human being assumes in this theory the exalted char- 
acter of a fellow-laborer with the Highest, a fellow-combatant 
in the great strife ; contributing his little, which by the aggre- 
gation of many like himself becomes much, towards that pro- 

35 Ibid., pp. 112 f . 

36 IMd., pp. 176 ff. 



28 The Argument for a Finitist Theology. 

gressive ascendancy, and ultimately complete triumph of good 
over evil, which history points to, and which this doctrine 
teaches us to regard as planned by the Being to whom we owe 
all the benevolent contrivance we behold in Nature." 37 

Mill's position is enthusiastically endorsed by William 
James in his volume on A Pluralistic Universe. " When John 
Mill said that the notion of God's omnipotence must be given 
up if God is to be kept as a religious object, he was surely ac- 
curately right; yet so prevalent is the lazy monism that idly 
haunts the region of God's name, that so simple and truthful 
a saying was generally treated as a paradox. God, it was said, 
could not be finite. I believe that the only God worthy of the 
name must be finite." 38 With all its ambiguities and incon- 
sistencies, the common conception of God is at bottom that of 
a finite Being. The God of David or of Isaiah, the Heavenly 
Father of the New Testament, is not the Absolute. " That 
God," says James, " is an essentially finite being in the cosmos, 
not with the cosmos in him." " The God of our popular 
Christianity is but one member of a pluralistic system. He 
and we stand outside of each other, just as the devil, the saints, 
and the angels stand outside of both of us." 39 

Mill's polemic is directed against the doctrine of omnip- 
otence as held by traditional orthodoxy; that of James is di- 
rected against the conception of the Absolute, which has been 
supposed by its adherents to solve difficulties such as those 
raised by Mill. 40 "The absolute," insists James, "taken 
seriously, and not as a mere name for our right occasionally to 
drop the strenuous mood and take a moral holiday, introduces 
all those tremendous irrationalities into -the universe which a 
frankly pluralistic theism escapes, but which have been flung 
as a reproach at every form of monistic theism or pantheism. 
It introduces a speculative ' problem of evil' namely, and 

3T Ibid., p. 117. 

38 James, A Pluralistic Universe, p. 124. 

39 Ibid., pp. 110 f. j see also The Will to Believe, pp. 116 and 134 f. 

40 Religious Aspect of Philosophy, p. 453 ; Sources of Beligious Insight, 
pp. 240 ff. 



The Doctrine of a Finite God. 29 

leaves us wondering why the perfection of the absolute should 
require just such hideous forms of life as darken the day for 
our human imaginations. If they were forced upon it by 
something alien, and to l overcome' them the absolute had 
still to keep hold of them, we could understand its feeling of 
triumph, though we, so far as we were ourselves among the 
elements overcome, could acquiesce but sullenly in the resultant 
situation, and would never just have chosen it as the most 
rational one conceivable. But the absolute is represented as 
a being without environment, upon which nothing alien can 
be forced. . . . Its perfection is represented as the source of 
things, and yet the first effect of that perfection is the tre- 
mendous imperfection of all finite experience." 41 

To this the partisan of the Absolute will, of course, object 
that the imperfection of the finite is a logically indispensable 
condition of the perfection of the Infinite. And not only the 
monistic idealist, but the defender of traditional theology may 
take this position. Thus St. Augustine long ago taught that 
evil does not disturb the order and beauty of the universe ; for 
" as a painting with dark colors rightly distributed is beau- 
tiful, so also is the sum of things beautiful for him who has 
power to view them all at one glance, notwithstanding the 
presence of sin, although, when considered separately, their 
beauty is marred by the deformity of sin. God would not have 
created those angels and men of whom he knew beforehand 
that they would be wicked, if he had not also known how they 
would subserve the ends of goodness." " The whole world 
thus consists, like a beautiful song, of oppositions." 42 Or, to 
employ an illustration of the Platonic-Augustinian doctrine 
which is repeated by Eoyce, " as one looking over the surface 
of a statue with a microscope, and finding nothing but a stony 
surface, might say, how ugly! but on seeing the whole at a 
glance would know its beauty ; even so one seeing the world by 
bits fancies it evil, but would know it to be good if he saw it 

4i A Pluralistic Universe, p. 117. 

42 Ueberweg, Geschichte der Philosophie, 161 f . 



30 The Argument for a Finitist Theology. 

as a whole. And the seeming but unreal evil of the parts may- 
be necessary in order that the real whole should be good." 43 

This, however, is not precisely the view of Royce himself. 
He is not content to say that the evil must exist to sdt the 
good off by way of contrast. He maintains that the " evil will 
is a conquered element in the good will, and as such is neces- 
sary to goodness." "Goodness . . . has as its elements the 
evil impulse and its correction. The evil will as such may be 
conquered in our personal experience, and then we are our- 
selves good ; or it may be conquered, not in our thought con- 
sidered as a separate thought, but in the total thought to which 
ours is so related, as our single evil and good thoughts are 
related to the whole of us. ... As the evil impulse is to the 
good man, so is the evil will of the wicked man to the life of 
God, in which he is an element." 44 

The doctrine which we have found in the earliest of Pro- 
fessor Royce's books is found also in those which appeared 
shortly before the end of his life. Thus in The Sources of 
Religious Insight he writes of evils " which cannot, yes, which 
in principle, and even by omnipotence, could not, be simply 
removed from existence without abolishing the conditions 
which are logically necessary to the very highest that we know. 
Life in the spirit simply presupposes the conditions that these 
ills exemplify. . . . Such sorrows, such idealized evils, which 
are so interwoven with good that if the precious grief were 
wholly removed from existence, the courage, the fidelity, the 
spiritual self-possession, the peace through, in, and beyond 
tribulation which such trials alone make possible, would also 
be removed, surely show us that the abstract principle : ' Evil 
ought to be abolished/ is false." 45 

Royce holds that a world like the one we know, which con- 
tains courage, fidelity, etc., and the evils which make these 
noble human qualities possible, is ethically preferable to a 

43 Beligious Aspect of Philosophy, p. 265. 
** Ibid., pp. 455 f . 

45 Sources of Beligious Insight, pp. 250 ff. See also The Problem of 
Christianity, I, 308 and elsewhere. 



The Doctrine of a Finite God. 31 

world which would contain no evil and therefore none of the 
virtues which presuppose it. For him the ideally perfect 
whole is not composed of none hut perfect parts. On the con- 
trary the imperfection of some of the parts is a logical con- 
dition of the complete perfection of the whole. To such rea- 
sonings, James replies that "the ideally perfect whole is cer- 
tainly that whole of which the parts also are perfect — if we 
can depend on logic for anything, we can depend on it for that 
definition." Is then a whole that consists of parts all of 
which are themselves perfect ethically preferable to a whole 
the perfection of which includes some imperfection, and, in- 
deed, consists at least in part in the overcoming of imperfec- 
tion ? Here we have the issue between the pluralistic and the 
monistic ethics in a nutshell. In the next chapter we shall 
consider this issue in so far as it is relevant to the problem of 
theodicy. 



IV. 

Theological Finitism as the Outcome of a Rational 

Theodicy. 

If the world is conceived in a pluralistic or dualistic 
fashion, the case for theological finitism is complete. Mill's 
argument is unanswerable. If we think of God as a Person 
who stands in moral relations with other persons, then, even 
if we assume these others to be his creatures, it is impossible 
to hold that he is omnipotent and at the same time perfectly- 
good. The notion of omnipotence is, in itself, logically unob- 
jectionable: it is logically possible to hold that the Supreme 
Being is omnipotent. But, if he is omnipotent, he is either 
malevolent or else non-moral. The Supreme Being might be 
one who would take pleasure in the sufferings of his creatures, 
only doling out to them sufficient satisfactions to induce them 
to continue the business of living ; or he might be wholly indif- 
ferent to their joys and sorrows. Such a being, however, 
would not deserve to be called God; for God, we say, is good. 
But if God is good, then he is not omnipotent. 

1. The Failure of Monistic Theodicy. — In this section I 
propose to show that, if we think of the world monistically , a 
rational theodicy is impossible. Let us then, for the present, 
ignore the logical and psychological difficulties of monistic 
idealism, except as we shall find them to be bound up with its 
ethical difficulties. Let us assume the monistic theory of the 
world and inquire concerning its treatment of the problem of 
evil. 

It is one of the merits of Royce's discussion that he insists 
upon finding a solution that shall be rational. He does not 
demand the right to make mutually contradictory statements 
about God, on the ground that it is about God that he is 

32 



Theological Finitism the Outcome of Rational Theodicy. 33 

speaking. He is not satisfied with saying that in some way 
that is wholly mysterious to us partial evil may be universal 
good. The PI atonic-August ini an analogy of the beautiful pic- 
ture which is composed of dark as well as light colors 46 is not 
satisfactory to him. It gives us no enlightenment as to why 
just these particular evils are necessary to make the perfec- 
tion of the whole. It suggests an ethics of quietism; for it 
logically implies that the distinction between good and evil is 
mere appearance and not genuinely valid. 

For Royce, then, evil is not merely " an illusion of the par- 
tial view; . . . but . . . seems in positive crying opposition 
to all goodness." " We do not say that evil must exist to set 
the good off by way of contrast. . . . We say only that the 
evil will is a conquered element in the good will, and is as 
such necessary to goodness." " The good act has its existence 
and life in the transcending of experienced present evil." 
" Goodness as a moral experience is for us the overcoming of 
experienced evil; and in the eternal life of God the realiza- 
tion of goodness must have the same sort of organic relation to 
evil as it has in us." 47 According to the theory of monistic 
idealism, then, evil has its place in the perfect world. It is 
the condition of the possibility of the good. Even the worst 
conceivable evil, the deed of a traitor, may be the condition of 
an atoning deed by which the world is so re-created and trans- 
formed that it is " better than it would have been had all else 
remained the same, but had that deed of treason not been done 
at all." 48 

Now no one will question the reality and importance of the 
experiences and social situations employed to illustrate the 
" overcoming " of evil. Physical pain sweetens and sanc- 
tifies the life of those who accept it resignedly, and bear it 
patiently. One who meets his troubles bravely may thus make 
them stepping-stones to a level of character which he could not 
otherwise have attained. As we study the record of human 

46 See Chapter III. 

47 The Religious Aspects of Philosophy, pp. 456 ff. 

48 The Problem of Christianity, I, 308. 



34 The Argument for a Finitist Theology. 

progress, we frequently meet cases in which an act of sin seems 
to have been the indispensable condition of great good. The 
conception of the " overcoming " of evil is then undoubtedly a 
conception of great significance. Nevertheless, the theodicy 
offered by monistic idealism is not satisfactory. The monistic 
theodicy fails for two reasons : (a) It does not account for all 
evils; and (b) its account of evil tacitly presupposes a 
pluralistic view of the world. 

(a) If the only evil were an evil will, and the only good a 
good will, then the notion of the " overcoming " of evil would 
be much less unsatisfactory. Let us grant for the sake of the 
argument, that the will may be good or evil in itself, that is to 
say, without reference to the consequences likely to flow from 
its choices (a theory which is, however, very hard to under- 
stand). But, even if we grant that will may be good or bad 
per se, there is no reason to hold that there are no other goods 
and evils. The enumeration of " goods " is a sort of personal 
confession of faith. ~No ultimate rational ground can be given 
for calling anything good or bad. The perception of values is 
a presupposition of all reasoning about right or wrong, good 
or bad. Certainly, no one will claim that the goodness or 
badness of will can be logically demonstrated. And all that I 
am insisting upon here is, that, if we recognize good or bad 
will, we are also justified in speaking of other "goods" and 
"evils." 

One of these other goods is pleasure, and one of these other 
evils is pain. Now it is true that in many cases pain sub- 
serves a good purpose, and that the patient endurance of pain 
(and, still more, I should say, the effort to relieve and destroy 
it in oneself and in others) evokes some of the most admirable 
human qualities ; but no one has proved that all pains are pro- 
ductive of sufficient good to justify their existence, and, as we 
shall see below, this attempted justification of pain presup- 
poses a non-monistic view of the world. 

Another " good " is life, considered apart from its pains and 
pleasures. The corresponding " evil " is death, especially pre- 



Theological Finitism the Outcome of Rational Theodicy. 35 

mature death. An earthquake destroys a thousand men; a 
child, previously strong and healthy, falls a prey to a con- 
tagious disease, in consequence of the ignorance or careless- 
ness of its parents and the negligence of the community. If 
the life of the person has ceased, he cannot be said to havfe 
been strengthened or ennobled by the misfortune that has 
befallen him. If, on the other hand, we assume that the per- 
son is immortal, and that his moral development continues in 
spite of what we call death, there is no reason for holding that 
his character has been improved by his unfortunate experience, 
or that it was in any sense good for him that his entrance into 
the next world should have been hastened through human 
ignorance and sin. In either case, there is no reason for be- 
lieving that the perfection of the Absolute requires the termi- 
nation of human lives in this manner. 

Another " good " 'is sound intelligence, and the correspond- 
ing " evil," insanity. This presents an especially difficult case 
for the monistic idealist. The physical life continues, but all 
opportunity for moral achievement is cut off. The evil is 
surely not overcome in the individual, and there is no reason 
for supposing it to be overcome in the Absolute, unless, indeed, 
one is willing to hold that mere variety of content is to be 
so highly esteemed, that the content of the perfect Mind must 
be assumed to include the insane delusions of these unfor- 
tunates. Very similar considerations confront us when we 
think of those cases in which men's wills have been weakened 
by disease ; or in which immature moral agents are compelled 
by economic conditions to live in an environment that is con- 
ducive to sin. 

Now so long as there remains a single evil that cannot ra- 
tionally be supposed to be "overcome," or even that cannot 
be rationally shown to be overcome, we must conclude that the 
monistic theodicy has failed. It is, of course, possible to find 
a great many cases in the life of the race, as also in the ex- 
perience of the individual moral agent, where evil seems to 
have been thus overcome. But these cases may be matched 



36 The Argument for a Finitist Theology. 

with others where just the contrary seems to be true. The 
" treason " of the sons of Jacob led eventually to the elevation 
of their brother to the virtual kingship of Egypt, and to the 
preservation of the whole Israelite clan from famine ; but the 
assassination of Abraham Lincoln led to bitter days in the 
life of the American people, which, there is reason to believe, 
might have been shortened or prevented, if the great President 
had been permitted to live a few years longer. To be sure, we 
do not know what the course of events would have been, had 
Lincoln served out his second presidential term; but neither 
do we know what the course of events would have been, if 
the brethren of Joseph had never sinned, or if Judas had not 
betrayed his Lord. 

As we look back over our lives, we see temptations over- 
come and difficulties bravely met and conquered; but what 
shall we say of the temptations that were not overcome, of the 
difficulties that were not conquered ? 

Professor Koyce himself speaks of a class of evils that, so 
far as we can see, are not overcome. " Pestilence, famine, the 
cruelties of oppressors, the wrecks of innocent human lives by 
cruel fortunes — all these seem, for our ordinary estimates, 
facts that we can in nowise assimilate, justify, or reasonably 
comprehend. ... To such evils, from our human point of 
view, the principle : ' They ought to be simply driven out of 
existence,' is naturally applicable without limitation." 49 

These evils, then, are not seen to be necessary to the per- 
fection of the universal good. They are not yet "spiritual- 
ized." But, then, with respect to all such evils, the theodicy 
is not rational. Unfortunately, philosophy must be written 
" from our human point of view." So far as these evils are 
concerned, we are no farther on than were Plotinus or Augus- 
tine. All we can say is that, in spite of certain ugly black 
spots, the picture may be beautiful as a whole for a Mind that 
can behold it thus. 

(b) Our second reason for rejecting the monistic theodicy 

49 Sources of Religious Insight, p. 233. 



Theological Finitism the Outcome of Rational Theodicy. 37 

is that it tacitly presupposes a pluralistic view of the world. 
What can we make of the claim that evil is " f ragmentari- 
ness " ? Is fragmentariness, as such, evil ? Then nothing is 
really good except the Whole ; and the contrast of " good " and 
" bad " is identified with the contrast between the " more in- 
clusive " and the " less inclusive." But why the more inclusive 
should be regarded as better, and the all-inclusive as best of 
all, is by no means clear. 

Well, then, does " overcoming " mean more than the mere 
relation of Whole to part? If it is to have any ethical sig- 
nificance, it certainly must mean more than this. Some parts 
of the Absolute, to wit good men and good impulses, are 
" good " ; others are " evil " ; and this difference is not a dif- 
ference of size, or of complexity of organization. There is 
here a genuine difference of character; and therefore if the 
notion of " overcoming " is to have any moral significance at 
all, the evil that is overcome must be not merely a part of the 
Absolute, but a something other than the Absolute. For this 
reason James is right in saying that the ideally perfect whole 
is that whole of which the parts also are perfect. 50 It may 
not be true that the ideally perfect world, or the ideally per- 
fect group of moral agents, is that world or group all the parts 
of which are perfect; but this is true of a whole; for within a 
whole it is logically impossible for good and evil to come into 
conflict. Moral " overcoming " implies a conflict of persons, 
or at least of numerically distinct forces, tendencies, or im- 
pulses; and not merely a contrast of parts with one another 
or with their Whole. 

Furthermore, if monistic idealism is not to give us an ethics 
of acquiescence, if the notion of " overcoming " is to be taken 
seriously, we must assume the reality of temporal succession. 
All the illustrations of the overcoming of evil, the case of the 
traitor and all cases in which a person is strengthened and en- 
nobled by misfortune, imply the notion of time. If it were 
possible to assign any meaning at all to the notion of a time- 
so The Pluralistic Universe, p. 123. 



38 The Argument for a Finitist Theology. 

less act, it might be possible to think of an eternal prevention 
of evil ; but not of an eternal overcoming of evil. 

2. The Outline of a Finitist Theodicy. — In so far, then, 
as the conception of " overcoming " is valid and morally sig- 
nificant, it presupposes a finitist theology. If we no longer 
try to think of God as all-inclusive, and no longer think of 
him as omnipotent, then this conception of the logical neces- 
sity and practical value of evil is a conception of great im- 
portance. But we need not affirm that all evils are necessary 
for the perfection of the world. We may admit the reality of 
stern and opaque necessities, which can not be transcended, 
which are not completely understood, it may be, by the Su- 
preme Person himself. 

The theological finitist may say without logical inconsistency 
that it is better that there should be sin than that no oppor- 
tunity should be afforded for freedom and personality. 

He may say that it is better that the operations of Nature 
should be uniform, than that Nature, like an over-kind nurse, 
should be continually stepping in to shield us from the results 
of ignorance, recklessness, or indolence. 

He may say that some of the evils which we endure are the 
condition of the prevention of greater evils. He may, there- 
fore, without inconsistency, explain much of our physical pain 
as a warning against courses of action that would lead to 
greater misery. 

He may expatiate upon the educative function of suffering 
of every description, and show how its patient endurance, 
when it is irremediable, will produce a beautiful and saintly 
character. 

In short, the theological finitist may take over into his sys- 
tem of thought all the particular instances of " compensation," 
but need not attempt to show that the "compensation" is 
complete or universal. Many evils exist which ought to be 
" simply destroyed " ; but God is not strong or wise enough, 
and certainly we are not, to destroy them immediately. In 
other words, the finitist may take seriously the thought of 



Theological Finitism the Outcome of Rational Theodicy. 39 

evolution or progress — a conception which the absolutist is 
logically forbidden to entertain. 

"We have found a thought/' says Royce in his first philo- 
sophical book, " that makes this concept of progress not only 
inapplicable to the world of the infinite life, but wholly super- 
fluous." " Progress in this world as a whole is therefore sim- 
ply not needed." 51 For the theological finitist, on the con- 
trary, the concept of progress, far from being " superfluous," 
is of immense significance. He hopes for, and believes in the 
possibility of, a better world ; and, while lamenting the logical 
inconsistency of his monistic brother, works by the side of the 
latter in the effort to hasten the coming of this better world, 
si The Religious Aspect of Philosophy, pp. 464, 466. 



Logical Finitism and the Idea of God. 

In the preceding chapters we have come to the conclusion 
that it is impossible to think of God as infinite in the first of 
the two senses of the word. (See Chapter I, Section 4.) The 
hard facts of human experience forbid us to say that God is 
the Whole of reality, or that he is omnipotent. In the present 
chapter I wish to discuss the arguments of a school of thinkers 
who have maintained the logical absurdity of holding that 
God is infinite in the second of our two senses. According to 
these thinkers we cannot say without self-contradiction that 
God (or the world, or anything) consists of or includes an 
infinite multiplicity of elements, or perdures through an in- 
finite sequence of moments. While this theory and the view 
which I have called " ethical finitism " do not imply each 
other, inasmuch as they deny the infinity of God in two dif- 
ferent senses, yet these two kinds of finitism are mutually com- 
patible, and support one another, since both are opposed to 
monistic idealism, which maintains that God, or the Absolute, 
is infinite in both senses. 

The founder of this school of thinkers was Charles Eenou- 
vier (1815-1903), who is said by James to have been the 
" strongest philosopher of France in the second half of the 
nineteenth century." 52 As important disciples we may name 
F. Pillon, F. Evellin, and E. Boutreux. Henri Bergson, 
France's most eminent living philosopher, has been greatly in- 
fluenced by Bcnouvier, but it would scarcely be just to call 
him a disciple. 53 

" Neocriticism," as the Renouvierist philosophy is called in 

52 Problems of Philosophy, p. 163. This, the last book of William James, 
is dedicated "to the great Kenouvier's memory." 

53 Thilly, History of Philosophy, pp. 511 f . 

40 




Logical Finitism and the Idea of God. 41 

recognition of its historic relation to the system of Kant, is 
characterized by Windelband as a synthesis of Kant and 
Comte. Kenouvier, however, while no doubt influenced by 
Comte, always emphasized the difference between his own 
philosophy and positivism. Positivism begins with a discus- 
sion of the natural sciences and of the implications of scientific 
method, and is led to a rejection of the notions of being-in- 
itself and transitive cause. Neocriticism reaches a similar 
conclusion by a different road. It "begins with the logical 
investigation of mental phenomena, . . . and completes the 
Humian critique of the concepts of substance and causality 
by means of an apriorism related to that of Kant: in mental 
phenomena we have to seek ' essentially ' the laws of all being. 
Thus neocriticism is indeed phenomenalism, but not empiri- 
cism." 54 

1. The Finitist View of the World. — The best introduction 
to the philosophy of Eenouvier is a study of the Kantian " an- 
tinomies." According to the first of these it can be proved 
that the world has a beginning in time and limits in space; 
and it can be proved with equal cogency that it has no begin- 
ning and no limits. The second antinomy affirms that every 
compound substance consists of simple, that is indivisible, 
parts; and also that there is nothing simple, but that every- 
thing is infinitely divisible. The third and fourth antinomies 
treat in the same way the issue of causality versus freedom, 
and the question of the existence of an absolutely necessary 
Being. 55 

There are certain obvious weaknesses or oversights in the 
demonstration. Yet it is possible so to revise Kant's argu- 
ments as to make them much more cogent. 56 If, then, the 
demonstration of both thesis and antithesis, in the case of each 
or only of some of these examples of the conflict of reason with 

•54 Windelband, Lehrbuch der Geschichte der Philosophie, S. 515 ; Feigel, 
Der Franzosische NeoTcriticismus, S. 9. 

«5 Kant, Kritik der Beinen Vernunft, A, 426-461 (Mueller, pp. 344 ff.). 

•56 See Kenouvier, Critique de la Doctrine de Kant, pp. 29 f . Cf . Les Di- 
lemmes de la M4taphysique Pure. 



42 



The Argument for a Finitist Theology. 



itself, be regarded as valid, the natural outcome might seem 
to be a thoroughgoing scepticism, an utter despair of the pos- 
sibility of attaining the right to be certain about anything. 
For if the human reason thus falls into necessary self-contra- 
diction, what ground have we for trusting it even in those cases 
in which no contradiction is discoverable? Such a complete 
scepticism, however, is practically impossible; and, accord- 
ingly, it is more common for those who hold that both the 
theses and the antitheses are valid to argue that the existence 
of these antinomies constitutes a reason for the subordination 
of the human reason to the authority of the Church or the 
Bible. From these necessary conflicts they conclude that 
human reason has its limits, that we are not always safe in 
refusing to believe some propositions, even though they appear 
to us to be logically absurd or self-contradictory. Difficulties 
and even self-contradictions may be found in the historic 
creeds, if we look for them ; but the same is true of some of 
the most commonly received conceptions, such as the notions 
of space and time. Therefore, these thinkers argue, we are 
justified in believing "mysteries," that is to say, in holding 
to the truth of propositions that are logically inconceivable. 57 
In one of his earliest philosophical works, Le Manuel de 
Philosophie moderns (1842), Charles Renouvier himself had 
thought it possible to believe both the theses and the an- 
titheses of these antinomies. 58 But the Essais de Critique 
generate began a polemic against this position; 59 and, in his 
mature philosophy, logical conceivability, that is to say, free- 
dom from self-contradiction, became the criterion, not only of 
all valid thinking, but also of real existence. Thus it is a car- 
dinal principle of the neo-criticist school that one of the two 
sides of each of the mathematical antinomies must be false. 
There is no meaning in saying that both are true. As Evellin 
puts it, " To say yes and no of the same thing at the same time 

57 See Mansel, The Limits of Religious Thought; Newman, The Gram- 
mar of Assent; Hamilton, Lectures on Metaphysics. 

■58 Arnal, Philosophie Beligieuse de Charles Renouvier, p. 29. 
59 loid., p. 33. 



Logical Finitism and the Idea of God. 43 

and under the same point of view, this is contradiction; and 
for the understanding contradiction is death." 60 

Accordingly the neo-criticists recognize the principle of 
contradiction as the fundamental principle of thought. More- 
over, they refuse to exempt any topic of discussion whatever 
from the sway of this principle. You can't appeal to it in 
order to demolish the theories of other people, and then refuse 
to admit its universal validity when it threatens to demolish 
some pet theory of your own. This principle, they insist, is 
essential, not only to human intelligence, hut to intelligence 
as such. You may speak if you will of an intelligence that is 
higher than human ; but, unless the principle of contradiction 
is a principle of this higher intelligence also, the phrase 
"higher intelligence" is a phrase without meaning. Or, if 
you say that you believe in " truths above reason," which on 
the plane of human reason take the form of self-contradictory 
propositions, they will tell you that you are the dupe of words. 
Each of the words of a self -contradictory proposition may in- 
deed have a perfectly clear and definite meaning when taken 
separately, but the combination has no meaning, and the so- 
called proposition is, strictly speaking, no proposition at all, 
but merely a succession of words. You may believe that you 
believe it ; but in reality you do not believe it, for it is neither 
true nor false but meaningless. 

The principle of contradiction is thus the corner-stone of 
the Renouvierist philosophy. ISText in importance, and, as 
Renouvier and his disciples maintain, a necessary consequence 
of it, is the " principle of number." This is the principle that 
an infinite number is a self-contradictory notion, and that 
there can therefore be no actual infinite. Again and again in 
his voluminous writings 61 Renouvier recurs to this point, and 
seeks to establish it in various ways, but especially by an ex- 
amination of the properties of the series of cardinal numbers. 

60 Evellin, Infini et Quantite, p. 19. Cf . Kenouvier, Les Dilemmes de la 
Metaphysique Pure, pp. 2 f . 

6i See Les Dilemmes de la Metaphysique Pure, pp. 122-125; Nouvelle 
Monadologie, p. 35; Logique Generale, I, pp. 46 f., 57, and elsewhere. 



44 The Argument for a Finitist Theology. 

A typical illustration of the absurdity of supposing that an 
infinite unmber may actually be given is borrowed from the 
writings of Galileo. It runs as follows: 

" Suppose the series of natural numbers to be given. We 
can then form another sequence composed exclusively of the 
squares of the first, for it is always possible to find the square 
of a number. Thus, by hypothesis, the second sequence will 
have a number of terms equal to the number of terms of the 
first. Now the first contains all the numbers, squares as well 
as not-squares, while the second contains only the squares. 
The first has, therefore, a number of terms greater than that 
of the second, since, containing all the numbers, it contains all 
the squares, and it contains besides the numbers that are not 
squares. But by hypothesis or construction, these numbers of 
terms are equal. Therefore there are some equal numbers of 
which one is greater than another. But this consequence is 
absurd. Therefore it is absurd to suppose the natural series 
of numbers to be actually given." 62 Now if the natural series 
of numbers were given, it would of course be an actually in- 
finite multitude. But we have seen that it is absurd to sup- 
pose that the entire series of cardinal numbers is given; and, 
if this is true of the series of numbers, it is obviously true of 
every infinite series, since the terms of any series may be num- 
bered "one," "two," "three," etc. Therefore the notion of 
an actual infinite is absurd. In other words, every multitude 
has a number ; but the notion of an infinite number is logically 
impossible; and therefore it is impossible that there should 
be any actually existing infinite multitude. 

Here, however, an important distinction is to be made. We 

should discriminate between the notion of an infinite which is 

merely potential and that of an infinite in the absolute sense 

of the term. " The first consists in this : that, however great 

or small we assume a given entity to be, and however much we 

imagine it to be increased by repeated multiplications, there 

62Kenouvier, Les Principes de la Nature, p. 37; also Annee Philoso- 
phique, 1890, pp. 83 ff. 



Logical Finitism and the Idea of God. 45 

must still be thought to be something greater or smaller. The 
second infinite consists in this: that a thing has actually and 
absolutely so much magnitude or smallness that one can not 
imagine more of it." 63 The first infinite is called by Kenou- 
vier and his disciples the indefinite. Now the indefinite is a 
clear idea; but of the absolute infinite it is psychologically 
and logically impossible to form any conception. It is evi- 
dent from the above definition of the indefinite that it never 
is, but always becomes. Accordingly the indefinite may also 
be called the potential infinite. 

2. The God-Conception of the Logical Finitist. — Some of 
the theological implications of logical finitism are discussed 
by Pillon in the Annee Philosophique for 1890, in an article 
entitled " La Premiere Preuve Cartesienne De L'Existence 
De Dieu et La Critique De L'Infini." In this article, from 
which several citations have already been made, Pillon re- 
minds us that Descartes, after removing the doubt of his own 
existence by the help of the cogito ergo sum, seeks to escape 
from egoistic idealism by means of the idea of infinity or per- 
fection. The truth of our ideas about an external world is 
inferred from the existence of God ; and the existence of God 
is inferred from our possession of the idea of God. 

"Among my ideas there is one which represents a God, 
sovereign, eternal, infinite, immutable, omniscient, and uni- 
versal creator of the things which are outside of him." This 
idea, says Descartes, must have a cause ; and Descartes assumes 
that there must be at least as much " reality " in the efficient 
cause as in its effect. No idea can contain more objective 
reality than the formal reality of its cause. Now, the only 
cause adequate to the production of this idea of God, which we 
find in our minds, is God. Therefore God exists. Therefore 
the external world is a real world. Such is Descartes's 
reasoning. 

Pillon remarks that, in assuming the general proposition 
that the effect can not be superior to the efficient cause, Des- 

63 L 'Ann6e Philosophique, 1890, p. 56. 



46 The Argument for a Finitist Theology. 

cartes reveals a failure to make his original doubt as uni- 
versal as he supposed he had made it. 64 If, with the school 
of Kenouvier, we hold that there may be first beginnings, that 
is to say, uncaused events, it is evident that there is no neces- 
sity for believing that the effect can contain no more " reality " 
than the cause. For, in so far as the scholastic principle is 
regarded as demonstrable, it rests upon the assumption that 
every event must have a cause. The scholastic philosophers 
reasoned, and after them Descartes, that if the effect con- 
tained more reality than the cause, then, assuming that both 
effect and cause are divisible into parts, some parts of the 
effect would be uncaused, since the more real being would 
have the greater number of parts. If, however, we assume 
that there is no necessary connection between the notion of a 
beginning and that of an effect, the scholastic principle as- 
sumed by Descrates sinks to the level of a pseudo-axiom. 
Accordingly, even if we do possess the idea of an infinite and 
perfect being, we are not justified in arguing from the fact of 
its possession to the existence of such a being. 

Moreover, says Pillon, Descartes confused the notions of 
infinity and perfection. Descartes assumes the synonymity 
of the words " infinite " and " perfect." But, " the idea of the 
perfect, which Descartes and after him Malebranche, Eenelon, 
Leibniz, all the spiritualist philosophers of the eighteenth 
century, as all those of our time, have always confounded 
with that of infinity, should be rigorously distinguished from 
it. This distinction is one of the fundamental theses of the 
phenomenalist criticism." 

" Perfection is a general idea, formed from the ideas of 
diverse qualities of an excellence such as we contemplate with 
unmixed satisfaction, and to which we judge nothing that we 
can imagine of the same order to be preferable. These qual- 
ities are intellectual or moral or even physical: Such are 
knowledge, wisdom, justice, goodness, happiness, beauty, etc. 
A perfect being is a being in which these qualities are united," 

64 L 'Annee PhUosophique, 1890, p. 161. 



Logical Finitism and the Idea of God. 47 

and so fittingly and harmoniously combined that there is no 
occasion for " reproach or desire." " The ideas relative to 
perfection and those which concern mathematical magnitude 
form, in reality, two separate and irreducible categories." 
These categories rest upon two kinds of comparison: Com- 
parison of quantity and comparison of estimation or pref- 
erence. 65 The notion of perfection is then one which we can 
make for ourselves. Consequently, we do not need to assume 
the existence of a perfect being in order to explain the pres- 
ence of the idea in our minds. 

The notion of infinity, i. e., of infinity in the absolute sense, 
we can not make. But, says the neo-criticist, we do not really 
possess this notion, because it is logically contradictory. The 
causal relation of our notions of infinity is just the opposite 
of that supposed by Descartes. "It is not the idea of the real 
and absolute infinite impressed in our soul by this infinite, 
which explains the formation of our ideas of potential infinites. 
It is our ideas of potential infinites drawn from ourselves, 
which have conducted us by a process logically illegitimate, 
but psychologically natural, to the idea of the real and absolute 
infinite. It is the infinites, apparently actual, of the spatial 
and temporal world that have led us to the divine attributes." 66 

We can not, therefore, have any valid conception of infinity 
in the absolute sense. The world is finite and God is finite. 

3. The Attributes of the Finite God. — The idea of God 
which was supposed by Descartes to have been impressed by 
the Creator upon every human mind represented God as " sov- 
ereign, eternal, infinite, immutable, omniscient, omnipotent." 
The neo-criticist " principle of number," as we have seen, com- 
pels a revision of this idea. 

By Pillon, as by Royce, 67 omnipotence is treated as the 
typical attribute of Deity. We may justify this method of 
procedure on the ground that, in the first place, omnipotence 

es ibid., pp. 51, ill ff. 

66 Hid., p. 110. 

67 See Chapter II. 



48 The Argument for a Finitist Theology. 

implies omniscience; knowing is only a particular kind of 
doing. Not to know and not to be able to find out would be 
not to be able to do. In the second place, and conversely, om- 
niscience implies omnipotence. That knowledge is power is 
attested by the etymological affinity of the German konnen 
and kennen, and the English can and cunning, and by the uses 
of the French verb savoir. To know how is the same thing as 
to be able. An omniscient being, accordingly, will know how 
to do all things, that is to say, will be able to do all things, will 
be omnipotent ; and, on the other hand, if logic forbids us to 
think of God as omniscient, then we can not logically think 
of him as omnipotent either. 

Pillon approaches the discussion of the divine omniscience 
from the side of perfect foreknowledge. The problem is to 
reconcile the idea of perfect foreknowledge with the neo- 
criticist principle of number, and this reconciliation is, of 
course, impossible. 

Objection has frequently been made to the idea of a fore- 
knowledge of "free" acts. But the objection which Pillon is 
urging holds against the foreknowledge of determined events 
as well. For " these necessary or determined future events do 
not form a whole, a determined number, since they are sup- 
posed to produce themselves in a time which has no limits. It 
is an endless series, not simply of possibles, but of necessaries. 
It is necessary to say that the potential infinity of these future 
events finds itself in some manner realized in the divine under- 
standing; or else it is necessary to reject the perfect and abso- 
lute foreknowledge even when it is a question of necessary 
future events." 68 

Yet we may distinguish two sorts of omniscience, or in the 
special case just now in question, of perfect foreknowledge, 
corresponding to the distinction previously made between the 
absolute, or actual infinite and the potential infinite. There 
is, accordingly, a sense in which it is logically unobjectionable 
to speak of perfect foreknowledge. "Does it follow then," 

es iud., p. 174. 



Logical Finitism and the Idea of God. 49 

concludes Pillon, "that one ought to regard as impossible the 
perfection of foreknowledge ? Yes, assuredly, if one makes 
this perfection consist in the knowledge of an infinite number 
of future realities. No, if in place of attributing to the being 
who is supposed to be perfect a "single infinite and eternal 
thought," one admits that his intelligence differs from ours by 
its extent, and not in respect of its nature; that it proceeds 
like ours by separate and successive acts of thought ; that it is 
free to push back successively the limits of its horizon, but that 
it is always obliged to have a horizon. Thus understood om- 
niscience presents no contradiction." 69 In other words God 
might, so far as the purely logical argument is concerned, be 
assumed to be omniscient, in the sense of knowing all that is 
at any given moment knowable, even if he is finite in the sense 
of the neo-criticist. 

Accordingly, the view of Mill and James and of the previous 
chapter is not logically bound up with that of Kenouvier and 
Pillon. Logical finitism suggests and makes room for, but 
does not in itself require ethical finitism. As has already been 
said, our reasons for denying the divine omnipotence and om- 
niscience are not merely logical ; they are chiefly ethical. Yet 
the neo-criticist argument prepares men's minds for the ac- 
ceptance of this ethically grounded argument. Both argu- 
ments presuppose loyalty to the principle of contradiction, 
and both presuppose a certain freedom from the traditional 
preference for such words as " infinite," " omniscient," " om- 
nipotent," etc., when employed as adjectives modifying the 
word "God." 
«» ma., p. 179. 



VI. 

Theology and the "New Infinite." 

When Renouvier wrote his principal works he could say 
that the mathematicians were all agreed in rejecting the 
notion of an infinite number. As Arnal remarks, 70 " All the 
mathematicians who had weighed the terms of the alternative 
. . . were unanimous. All from Galileo to Cauchy had em- 
phasized the impossibility of the infinite of quantity, the ab- 
surdity of the realized infinite. . . . Why should that which 
is impossible and absurd from the point of view of mathematics 
be maintained from the point of view of metaphysics ? " 

Since the middle of the last century, however, the math- 
ematicians have been more favorably disposed towards the 
quantitative infinite, and the neo-criticists' appeal to the con- 
sensus of all mathematicians " from Galileo to Cauchy " is met 
by the counter-appeal to a rival consensus of philosophical 
mathematicians and mathematically-minded philosophers 
from Bolzano to Bertrand Russell. In the judgment of sev- 
eral contemporary thinkers one of the great achievements of 
the latter half of the nineteenth century was the discovery of a 
new definition of infinity, which, it is maintained, frees the 
conception from all the difficulties and puzzles found in it as 
formerly defined. 

1. The New Definition of Infinity. — The " new " definition 
of infinity is an incident, perhaps the culminating incident, 
in the "generalization" of the concept of number. 71 If we 
had only the finite whole numbers, 1, 2, 3, etc., while the fun- 
damental operations of addition, multiplication, and involu- 
tion would be in every case possible, the inverse operations 
would not be universally possible. For example, it would be 
impossible, if we had only such numbers, to subtract 3 from 

to La Philosophic religieuse die Charles Renouvier, p. 36. 
fiCouturat, Be L'Infini Mathematique, pp. 5-68, 281. 

50 



Theology and the "New Infinite/' 51 

2, to divide 2 by 3, or to find the square root of 3. In order 
that subtraction, division, and evolution may be universally 
possible, mathematicians have introduced the conception of 
negative numbers and zero, of fractional numbers, and of 
irrational and imaginary numbers. The definition of infinite 
or " transfinite " numbers should therefore be considered, not 
as an isolated incident, but as a part of this larger movement 
of mathematical thought. 

One of the discoverers of transfinite number was Georg 
Cantor. His theory of number is found in two memoirs which 
appeared in the Mathematische Annalen for 1895 and 1897 
under the title " Beitrdge zur Begrundung der Transfiniten 
Mengenlehre/ 7 These memoirs have been translated into Eng- 
lish by Philip E. B. Jourdain under the title of " The Theory 
of Transfinite Numbers/' 12 Cantor here defines the " power " 
or " cardinal number " of an aggregate M as " the general con- 
cept which, by means of our active faculty of thought, arises 
from M when we make abstraction of the nature of its various 
elements m and of the order in which they are given." If we 
do not make abstraction of the order, but only of the nature 
of the elements, the resulting concept is the ordinal number of 
the aggregate M. Two aggregates are equivalent, and there- 
fore have the same cardinal number, " if it is possible to put 
them, by some law, in such a relation to one another that to 
every element of each one of them there corresponds one and 
only one element of the other." 7 3 Employing the notions of 
an aggregate and of equivalence, together with the notions of 
"bindings" and "coverings," Cantor then defines the con- 
cepts of "greater" and "less," and the operations of addi- 
tion, multiplication, and involution. 74 

72 The Open Court Publishing Company, 1915. 

73 The Theory of Trans-finite Numbers, p. 86. 

74 Ibid., pp. 89-95. One aggregate is said to be greater than another 
(and therefore the cardinal number of the first greater than the cardinal 
number of the second) when (a) there is a part of the first which is 
equivalent to (i. e., can be put in one-to-one correspondence with) the 
second, but (b) no part of the second which is equivalent to the first (pp. 
89 ff.). 



52 The Argument for a Finitist Theology. 

This brings him to the discussion of the finite and trans- 
finite numbers. "Aggregates with finite cardinal numbers," 
he says, " are called ' finite aggregates ' ; and all others we 
call 'transfinite aggregates/ and their cardinal numbers 
'transfinite cardinal numbers.'" 75 The transfinite numbers 
are thus those that are not finite. We must therefore seek the 
distinguishing mark of the finite number. This is to be found 
in the following theorem : " If M is an aggregate such that it 
is of equal power with none of its parts, then the aggregate 
(M, e), which arises from M by the addition of a single new 
element e, has the same property of being of equal power with 
none of its parts." This theorem is used in establishing the 
fundamental properties of the " unlimited series of finite car- 
dinal numbers/' 76 and becomes a virtual part of their defini- 
tion. Finite aggregates, accordingly, are never equivalent to 
any of their parts, while transfinite aggregates may be. " The 
first example of a transfinite aggregate," continues Cantor, 
" is given by the totality of finite cardinal numbers ; we call 
its cardinal number ' Aleph-zero.' " The first transfinite car- 
dinal number is, then, the cardinal number of the " totality " 
of finite cardinal numbers. 77 

It should be noted that Cantor calmly assumes the logical 
tenability of this notion of the "totality" of an unlimited 
series, and as we shall presently see this is the crux of the 
whole matter. Just now, however, it is our purpose to under- 
stand the doctrine rather than to criticize it. 

A further advance in the theory of number ought next to be 
noted. Cantor, as we have seen, defined "cardinal number" 
and "ordinal type" as "general concepts which arise by 
means of our mental activity." Frege, in his Grundlagen der 
Arithmetic of 1884, defined "the number of a class u" as "the 
class of all these classes which are equivalent to tz," The same 
definition was discovered independently by Bertrand Kussell. 
" The two chief reasons in favor of this definition," says Jour- 

75 Hid., p. 103. 

76 ma., pp. 97-103. 

77 ma., p. 103. 



Theology and the "New Infinite/' 53 

dain, " are that it avoids, by a construction of ' numbers ' out 
of the fundamental entities of logic, the assumption that there 
are certain new and undefined entities called l numbers ' ; and 
that it allows us to deduce at once that the class defined is not 
empty, so that the cardinal number u exists in the sense de- 
fined in logic; in fact, since u is equivalent to itself, the car- 
dinal number of u has u at least as a member." 78 Cantor's 
definition of an infinite or transfinite number accordingly be- 
comes "the class of all classes that are similar to parts of 
themselves." 79 

The "New Infinite" was independently discovered by 
Eichard Dedekind. 80 His definition runs as follows: 81 "A 
system 8 is said to be infinite when it is similar to a proper 
part of itself; in the contrary case, 8 is said to be a finite 
system." 

The words "system," "similar," and "proper part" are 
employed in a technical sense, and require some explanation. 
A collection of objects is called a system (also by different 
writers an aggregate, manifold, or set) when it fulfils the fol- 
lowing conditions: 82 

(1) It includes all the objects to which a definite quality 
belongs. 

(2) It includes no object which does not possess this 
quality. 

(3) Each of the included objects is permanently the same, 
and distinct from all the others. These separate objects are 
called elements. In Dedekind's terminology, every system is 
a part of itself; while a system which contains some, but not 
all, of the elements of a given system is a proper part of the 
given system. The notion of similarity is identical with Can- 
tor's "equivalence," and exactly the same meaning is con- 
's rbid., pp. 202 f . 

to Russell, Principles of Mathematics, pp. 262, 321. 

&o Essays on the Theory of Numbers, p. 41. This is a translation by 
W. W. Beman of Dedekind's papers on " Stetiglceit und irrationale 
Zahlen" and "Was sind und was sollen die Zahlen." 

*ilbid., p. 63. 

82 Cf. Encyclopedia Britannica, 1910, Article on Number. 



54 The Argument for a Finitist Theology. 

veyed by the phrase " one-to-one correspondence." Any two 
groups or series are said to stand to each other in the relation 
of one-to-one correspondence when for each element or term 
of the one there is one and only one element or term of the 
other, and vice versa. To borrow an illustration from Mr. 
Russell, 83 " The relation of father to son is called a one-many 
relation, because a man can have only one father but may have 
many sons; conversely, the relation of son to father is called 
a many-one relation. But the relation of husband to wife (in 
Christian countries) is called one-one, because a man cannot 
have more than one wife, or a woman more than one husband." 

Dedekind's point is not that two systems which are assumed 
or already known to be infinite are similar or one-to-one corre- 
spondent, even if the one is only a part of the other. That 
such a similarity or equivalence is to be found between whole 
and part was, as we have seen, the very puzzle that had per- 
plexed the older mathematicians. The achievement of Dede- 
kind (if it is a genuine achievement) is rather the reversal of 
the method of attack. The " similarity " of whole and part is 
no longer merely an observed fact, nor is it for him an in- 
ference from their infinity; but infinity is now defined to be 
such similarity. If a system or aggregate is similar to a proper 
part of itself, then it is infinite; and this is the definition of 
an infinite system. 

2. The New Infinite and Logical Finitism. — It has been 
maintained by M. Couturat and others that Renouvier's 
critique of infinite number, and therefore his whole system of 
philosophy so far as it is based upon this critique, is founded 
upon an erroneous definition of the mathematical infinite. 84 
It accordingly becomes a matter of some importance to inquire 
into the merits of this "new" and, as is maintained, more 
correct definition. Our examination will lead us to the con- 
clusion that the "new" infinite is only the old infinite in a 
rather easily penetrable disguise ; that the definition of Dede- 

83 Scientific Method in Philosophy, p. 203. 
s* Be L 'Infini Mathematique, pp. 444 ff . 



Theology and the "New Infinite." 55 

kind and Cantor is the logical equivalent of the definition sug- 
gested by etymology; that, therefore, if the reasoning of the 
neo-criticists is sound as long as we use the old definition, their 
arguments lose none of their cogency when we substitute the 
definition formulated by the new school of mathematicians. 

If we had no other preceptor than etymology, we should at 
once conclude that the infinite is that which is limitless or in- 
capable of completion. The definition of infinity adopted by 
Kant in his account of the " First Conflict of the Transcenden- 
tal Ideas" appears to be no more than an elaboration of this 
notion of Vnendliclikeit. " The infinity of a series," he says, 
" consists in this, that it can never be completed by means of 
a successive synthesis." Or again, " The true transcendental 
concept of infinity is, that the successive synthesis of units 
in measuring a quantity can never be completed." 85 For Kant, 
then, the infinite is simply an,d literally the endless. 

Another definition which is of considerable historical im- 
portance is that of Bolzano. Professor Keyser paraphrases it 
as follows : 86 " Suppose given a class C of elements. Out of 
these suppose a series is formed by taking for first term one 
of the elements, for second term two of them, and so on. Any 
term so obtained is itself a class of elements, and is defined as 
finite. iSTow either the process in question will exhaust C or 
it will not. If it will, C is itself demonstrably finite ; if it will 
not, C is defined to be infinite." Bolzano is recognized as the 
initiator of the movement which led to the formulation of the 
much-heralded " Xew Infinite " ; and Keyser tells us in the 
article from which the above excerpt has been taken that Bol- 
zano's definition, although perhaps not so convenient in the 
actual practice of the mathematician, is in principle exactly 
equivalent to that of Dedekind. However this may be, it is 
clear that Bolzano's definition is exactly equivalent to that of 
Kant. The difference between the two is formal only. Kant 
employs the method of addition; Bolzano that of subtraction. 

ssKritik der Eeinen Vernunft, A, 426 and 432. (Mueller's translation, 
pp. 344, 348.) 

86 Journal, of Philosophy, etc., I, 33. 



56 The Argument for a Finitist Theology. 

The former is thinking of the completion of a somewhat that 
exists only as a scheme or plan; the latter is thinking of the 
depletion of an already existing class of elements. Yet the 
fundamental thought is the same in hoth: that which is in- 
finite is endless; and because it is endless, it is impossible 
either to construct anything so great as to equal it, or to take 
away from it anything so great as to exhaust it. 

Let us now examine the "new" definition of infinity as it 
has been formulated by Dedekind. " A system 8 is said to be 
infinite when it is similar to a proper part of itself." As a 
first step in my argument that this infinite is only the old 
infinite in a new suit of clothes, I shall show that whenever a 
series is found which is " similar to" that is to say, in one-to- 
one correspondence with, a proper part of itself, the series in 
question may be shown to be in several other kinds of corre- 
spondence with the same part; in fact, any sort of corre- 
spondence that one pleases to look for may be discovered ; and, 
furthermore, any scheme or plan of correspondence may be 
shown to be just as rigidly determined by law as any other — 
and specifically, as the scheme of one-to-one correspondence, 
which the partizans of the "New Infinite" have too hastily 
assumed to be the relation in which the two series eternally 
stand. 

Consider as a typical case the series of even numbers, 
which, by definition, is a proper part of the series of whole 
numbers, and yet is required to stand in one-to-one corre-; 
spondence with that series, by the law that each of its terms is 
a number twice the corresponding term of the series of whole 
numbers. This series illustrates the " similarity " of a system 
to a proper part of itself; and, therefore, by Dedekind's defi- 
nition, is infinite. But we find that any other correspondence 
than the one-to-one may be seen, if we wish to see it. This 
may be exhibited thus : 

(W) 1, 2, 3, 4, 5, 6, ••• 
k ' (P) 2, 4, 6, 8, 10, 12, ••• 



Theology and the "New Infinite/' 57 

(W) 1, 2, 3, 4, 5, ••• 

(P) 2,4, 6,8, 10,12, 14,16, 18,20, ••• 

(F) 1,2, 3,4, 5,6, 7,8, ••• 

(P) 2, 4, 6, 8, ..- 

(W) 1,2, 3,4, 5,6, 7,8, 

(P) 2,4,6, 8,10,12, 14,16,18, 20,22,24. ••• 

Case I is the case which has been supposed to be the situ- 
ation. In the other three cases we have respectively a one-to- 
two, a two-to-one, and a two-to-three correspondence. Now 
these other sorts of correspondence are determined by clear 
and definite rules, of exactly the same kind as, although a little 
more complicated than, the rule which determines the one-to- 
one correspondence. In Case II, let the rule be, that the sec- 
ond of the two terms paired with any one term of the whole 
series shall be four times that term ; in Case III the second of 
the two terms of (W) is the same number as the one term of 
(P) with which the two terms of (W) are bound up; in IV 
every two terms of (W) are bound up with three of (P), and 
the rule determining the correspondence is, that the last term 
of any given group of (P) shall be three times the last term 
of the corresponding group of (W). Now it is necessary to 
insist that the (P) of I, of II, of III, and of IV is exactly 
the same series. The "proper part," 2, 4, 6, 8, 10, 12, 14, 
16, ••-, is the "proper part" that is considered in each case. 
It has been shown, then, that the whole series stands to this 
proper part in these various relations of correspondence in 
exactly the same sense in which it stands to it in the relation 
of one-to-one correspondence. 

The proof that this is true of any proper part of the series 
of whole numbers that one may choose to consider, as for ex- 
ample, the series of multiples by 3, 4, etc., or of squares, cubes, 
etc., of the terms of the natural series of numbers, must be 
left to the ingenuity and patience of the reader. 87 He will 

87 In the typewritten copy of this dissertation, which may be found in 
the library of the Johns Hopkins University, I have considered these and 
other series in considerable detail, and have suggested formulae for several 



58 The Argument for a Finitist Theology. 

find that the correspondence of a whole and a proper part of 
itself, which has been taken as the essential notion in the 
"new" definition of infinity, turns out, when more closely 
scrutinized, to be a nose of wax ; it can be bent in any direc- 
tion that one pleases. 

How then shall we interpret Dedekind's definition, in the 
light of our examination of these examples of the relation of 
one-to-one correspondence of whole and part ? " A system 8 is 
infinite if it is similar to a proper part of itself." Does this 
mean (1) That the whole and the proper part in question are 
in one-to-one correspondence, and in no other, or (2) that the 
whole is in one-to-one correspondence with a proper part of 
itself, but is also related to the same part in accordance with 
other schemes of correspondence? 

If the former interpretation is correct, then, so far as I am 
aware, no genuine example of an infinite system has ever been 
adduced. At any rate, no example of an infinite system is re- 
vealed by an examination of the mutual relations of the various 
series of cardinal numbers. If this is the meaning of the 
definition, the class of all classes each of which is " similar " 
to a proper part of itself is a class without any members; for 
we have found that in every case where a one-to-one corre- 
spondence is discoverable, correspondences of other sorts are 
also discoverable. 

On the other hand, if the latter is understood to be the 
meaning of the definition, if the whole and its proper part are 
in a relation of one-to-one correspondence, and also in rela- 
tions of one-to-two correspondence, two-to-three correspond- 
ence, etc., then the definition is not new, but is logically iden- 
tical with or at all events necessarily implies the old definition 
of the infinite as the endless; for any endless series is inex- 
haustible, and, between two inexhaustible collections, it is al- 
ways possible to exhibit a one-to-one correspondence, or any 
sort of correspondence that one chooses to look for, inasmuch 

types of proper parts, by the use of which an "m-to-n. correspondence ■ ■ 
(m and n being any whole numbers) may be determined between the 
series of whole numbers and any given proper part. 



Theology and the "New Infinite" 59 

as, however far the pairing of terms or the correlation of 
groups may be carried, there can never be any dearth of part- 
ners or of groups of terms in either collection. 

We should expect, then, that the logical absurdity found by 
Renouvier in the conception of a " realized infinite " would 
not be removed by so simple an expedient as the re-phrasing 
of the definition of infinity. The creators of the "New In- 
finite " have indeed " taken the bull by the horns," 88 and have 
sought to escape the self-contradiction lurking in the notion 
of infinity by making this very self-contradiction the heart 
and center of their definition. But this does not remove the 
contradiction. Although it has been sugar-coated, it is still 
there ; and it is an obvious, though not infrequently neglected, 
logical requirement that, to quote the words of Poincare, " in 
defining an object we aflirm that the definition does not imply 
a contradiction." 89 

Now when Dedekind speaks of the endless series of cardinal 
numbers as a system, he tacitly imports the notion of finitude 
into his definition of infinity. For we naturally think of a 
system as a whole, a somewhat that is completely given. The 
self-contradiction appears even more clearly when we consider 
the phraseology of Cantor. His " infinite aggregate " is con- 
ceived as a "totality." Thus his first example of an infinite 
or transfinite aggregate is the " totality of finite cardinal num- 
bers." 90 But as he himself speaks of "the unlimited series 
of cardinal numbers," 91 it is clear that he has fallen into a 
self-contradiction, or else that in his usage the term " totality " 
is not to be understood in the same sense as in the arguments 
of the neo-criticist school. For, if the series of numbers is 
unlimited, what right have we to speak of it as a whole or a 
totality? If the word "totality" is understood in the sense 
in which it is employed by Renouvier and Pillon, its use in a 
definition of the number "Aleph-zero" would constitute a 

ss James, Problems of Philosophy, p. 176. 
89 Science et Methode, p. 162. 
»o The Theory of Transfinite Numbers, p. 103. 
9i Ibid., p. 99. 



60 The Argument for a Finitist Theology. 

begging of the whole question which is at issue between the 
finitists and the infinitists. If, however, when Cantor speaks 
of a "totality," he means no more than that the collection or 
series which he denotes by the term is determinate (that is, is 
so defined that it is in principle possible to distinguish it from 
every other collection or series and always possible to tell 
whether or not it includes any given term or collection of 
terms), then such a "totality" may be infinite in the old 
sense, that is to say, it may be endless. For example, we can 
always tell whether or not a given number belongs to the series 
of even numbers or to the series of odd numbers; and, inas- 
much as these series are thus logically distinguishable, there 
is a sense in which they are definite and thinkable unities; 
yet each of these series is endless, because, by the very law of 
its formation, however far it is continued, we must needs look 
for more and still more terms. Such determinate but endless 
series are, indeed, examples of Renouvier's " indefinite." But 
in Renouvier's terminology an " endless totality " would be a 
contradiction in terms. That is why a " realized infinite " is 
logically impossible. An infinite that was realized, a some- 
what actually existing and not merely a scheme or plan in 
process of realization, would be a totality in the sense that no 
part of it would be wanting; and yet as infinite it would be 
endless or unfinished. 

There may be, and no doubt are, many logically distinguish- 
able types of endless series; and accordingly it is perfectly 
legitimate for the mathematician to study these various types, 
and even to call them transfinite numbers if he wishes to em- 
ploy that terminology, and is not himself led astray by it. 
But unless we forget this ambiguity in the meaning of the 
term " totality," it is impossible to suppose that the definition 
of " transfinite number " has made any contribution whatever 
toward the solution of the logical difficulty found by the school 
of Renouvier in the conception of a " realized infinite." 

3. The New Infinite and Monistic Idealism. — We must 
next inquire what bearing, if any, these recent discussions of 



Theology and the "New Infinite/' 61 

the definition of infinity have upon the doctrine of the monistic 
Absolute. Monistic idealism, I have said, implies the con- 
ception of infinity in both senses. In our second chapter we 
saw that God cannot be conceived without contradiction to be 
infinite in the first sense — he cannot be regarded as including 
all reality; and now it is in order to consider the dependence 
of monistic idealism upon the notion of infinity in the second 
sense — upon the mathematical or numerical infinite. There 
are two ways in which monistic idealism implies the notion of 
a realized infinite: 

(a) The Absolute is said to be in possession of all time in 
an Eternal Now. " The real world of our Idealism has to be 
viewed by us men as a temporal order. For it is a world where 
purposes are fulfilled. . . ." But "this same temporal order 
is, when regarded in its wholeness, an Eternal Order. . . . 
The whole real content of this temporal order . . . is at once 
known, i. e., is consciously experienced as a whole, by the Ab- 
solute." 92 

This may perhaps mean that the temporal order is an " il- 
lusion of the partial view," that it belongs to the realm of mere 
appearance and not to that of genuine reality. We have 
already pointed out the difficulty of attaching any meaning to 
the proposition that time is illusory, 93 and need not repeat 
what has already been said. The sentences just quoted from 
Professor Royce are capable of another interpretation. When 
he says that the whole content of the temporal order is known 
at once, he himself explains the phrase at once as equivalent 
to in the same present. Now the present, he tells us, is some- 
times understood to be the mathematical line which separates 
the future and the past, and as a mere boundary to be without 
extent. Again the present " is any one temporal event, in so 
far as it is contrasted with antecedent and subsequent events, 
and in so far as it excludes them from coexistence with itself 
in the same portion of any succession." In the third place, 

»2Koyce, The World and the Individual, II, 134 and 138. 
»3 Chapter II, Section 2 (6). 



62 The Argument for a Finitist Theology. 

the present " is any portion of real time with all its included 
events, in so far as there is any reason to view it as a whole, 
and as known in this wholeness by a single experience." 94 
When Koyce says, then, that the whole temporal order is 
known at once, his meaning may he no more than that the 
whole temporal order is a whole. All time is present to the 
Absolute as a totum simul. 95 

Here, however, we meet the difficulty of the realized in- 
finite, of the totality of the unlimited. Royce seeks to justify 
the conception of the totum simul by regarding it as analogous 
to the "specious present" of the individual mind. We per- 
ceive the words of a phrase or a brief clause like " The curfew 
tolls the knell of parting day," not merely as successive, but 
also all at once, as a whole. In the same way the Absolute, 
thinks Royce, knows all the events of all time at once or as a 
whole. Many questions might be asked about the analogy of 
the " specious present " and the " totum simul." But we can 
not ask them here. I merely wish to stress the point that the 
idealistic doctrine of an Eternal ISTow must stand or fall with 
the logical possibility or impossibility of the realized infinite. 
For all time includes the unlimited past and the unlimited 
future ; and how can that which is unlimited be a whole ? 96 

(b) The argument for monistic idealism depends upon the 
assumption that a thing exists "just in so far as there is ex- 
perience of its existence." 97 This principle is a special appli- 
cation of the more general principle of the "internality of 
relations." If a "thing" is constituted by the relations in 
which it stands, then the attempt to define anything must in- 
evitably lead to an infinite regress; and the infinite regress is 
logically intolerable. This is the burden of Mr. F. H. Brad- 
ley's "Appearance and Reality/' The attempt to define any 
of the ordinary categories of thought, as substance, quality, 

9* The World and the Individual, II, 140. 

95 Ibid., p. 141. 

»6 Compare Chapter V, Section 2. 

97 The Conception of God, p. 43. 



Theology and the "New Infinite." 63 

relation, the self, etc., brings us to no final or satisfactory con- 
clusion, but merely produces an endless series. 

Critics of a realistic temper may cut the knot by denying 
the principle of the internality of relations. Koyce, however, 
is committed to this principle, and therefore seeks to avoid the 
difficulty by maintaining that the " infinite regress " is not a 
fatal defect. It is fatal, he holds, only when you take it term 
by term, i. e., successively; if you assume the infinite multi- 
tude or series of terms to be given all at once in one single 
purpose or plan, the infinity becomes harmless. 

How then is it possible to take the " infinite regress " all at 
once? The problem, thinks Royce, is solved for us in Dede- 
kind's definition of infinity. Thus the New Infinite becomes 
a main support of monistic philosophy. Idealism implies an 
infinite system, and the discovery of Dedekind permits us to 
think of the infinite not merely as endless but as an instance 
of self-representation. "Whatever considerations make for 
an idealistic interpretation of reality, become considerations 
which also tend to prove that the universe is an infinitely 
complex reality, or that a certain infinite system of facts is 
real. For idealism, in defining the Being of things as neces- 
sarily involving their existence for some form of knowledge, 
is committed to the thesis that whatever is, is ipso facto known 
(e. g., to the Absolute). . . . Since, however, the fact world 
even for idealism contains many aspects (such as the aspects 
called feeling, will, worth, and the like) which are not iden- 
tical with knowledge, although for an idealist they all exist 
as known aspects of the world, it follows that for an idealist 
the facts which constitute the existence of knowledge are 
themselves but a part and not the whole of the world of facts ; 
yet, by hypothesis, this part, since it contains acts of knowl- 
edge corresponding to every real fact, is adequate to the whole, 
or in Dedekind's sense is equal to the whole. Hence the 
idealist's system of facts must, by Dedekind's definition, be 
infinite; or for the idealist the real world is a self-represen- 
tative system, and is therefore infinite." 98 

98 ma., 40. 



64 The Argument for a Finitist Theology. 

Moreover, if we try " to conceive . . . the universe in real- 
istic terms as a realm whose existence is supposed to be inde- 
pendent of the mere accident that anyone does or does not 
know or conceive it, . . . it is possible to show that this sup- 
posed universe has the character of a self-representative sys- 
tem," that is to say, is infinite. Eor, " if the supposition is 
itself a fact, then, at that instant, when the supposition is 
made, the world of Being contains at least two facts, namely, 
F and your supposition about F" Call the supposition /. 
Then your universe is at least F + /. But, " this universe as 
thus symbolized, has not merely a twofold, but a threefold con- 
stitution. It consists of F and of /, and of their +, i. e., of 
the relation as real as both of them, which we try to regard as 
non-essential to the being of either of them, but which for that 
very reason, has to be supposed wholly other than themselves, 
just as they are supposed to be different from each other." 99 

" Hereupon, of course, Mr. Bradley's now familiar form of 
argument enters with its full rights . . . the -\- is linked to 
/ and to F and the ' endless fission' unquestionably ' breaks 
out.' The relation itself is seen entering into what seem new 
relations." 100 

Thus Boyce agrees with Bradley that every form of real- 
istic being " involves such endless or self-representative con- 
stitution " ; 101 that, in particular, realistic being breaks down 
upon the contradictions resulting from this constitution. 
Boyce, however, does not accept the view a that to be self- 
representative is as such to be self-contradictory." This con- 
clusion, he thinks, is obviated by the help of the definition of 
infinity as a self-representative system. The notion of "self- 
representation " permits us to take an infinite multiplicity all 
at once. 

Boyce illustrates his meaning in various ways. Some manu- 
facturers have ingeniously used a picture of the package in 
which their product is contained as a trade-mark, and have 

99 The World and the Individual, p. 538 f. 
ioo Ibid., p. 540. 
ioi Ibid., p. 542. 



Theology and the "New Infinite/' 65 

then placed this trade-mark as a label upon the package. But 
the package thus labeled with its own picture, inevitably re- 
quires the picture to contain for accuracy's sake ... a pic- 
ture of itself." 102 Or suppose that somewhere upon the soil 
of England there is a map of England. Suppose, further, 
that this map is a perfect representation, indicating every de- 
tail of the surface of England. It is clear that this map must 
contain a map of itself. 

The attempt actually to construct an accurate picture or a 
perfect map of the sort just described would indeed require 
an endless process and therefore be impossible of fulfilment; 
but, says Koyce, the plan itself is given all at once. " Math- 
ematically regarded the endless series of maps within maps, 
if made according to such a projection as we have indicated, 
would cluster about a limiting point, whose position would be 
exactly determined. Logically speaking their variety would 
be a mere expression of the single plan, ( Let us make within 
England and upon the surface thereof, a precise map, with all 
the details of the contour of its surface.' . . . The one plan 
of mapping in question necessarily implies just this infinite 
variety of internal constitution. . . . We are not obliged to 
deal solely with processes of construction as successive in order 
to define endless series." 102 " To conceive the true nature of 
the infinite, we have not to think of its vastness, or even nega- 
tively of its endlessness; we have merely to think of its self- 
representative character." 103 

Does this idea of " self -representation " escape the dif- 
ficulty of the " endless regress " ? The issue thus raised is in 
principle the same as that involved in the conception of the 
"totality" of an unlimited series; yet inasmuch as we have 
taken Professor Royce as the typical exponent of monistic 
idealism it seems proper to devote a few paragraphs to a dis- 
cussion of the illustration which he himself employs. "A 
map of England, contained within England, is to represent 

102 The World and the Individual, pp. 506 f. 

103 Hiooert Journal, I, 35. 



66 The Argument for a Finitist Theology. 

down to the smallest detail every contour and marking, natural 
or artificial, that occurs upon the surface of England." 104 The 
perfection of the map requires that there be a " one-to-one 
correspondence, point for point, of the surface mapped and 
the representation." In other words, if A is the surface 
mapped and A' the representation, "for every elementary de- 
tail of A, namely, a, b, c, d (be these details conceived as points 
or merely as physically smallest parts; as relations amongst 
the parts of a continuum, or as relations amongst the units of 
a mere aggregate of particles), some corresponding detail, a,', 
b', c r , d% could be identified in A', in accordance with the 
system of projection used." 

Let us consider first the notion of perfect representation 
where the copy is assumed to be smaller than the original, and 
then that of perfect ^/-representation. 

In the opinion of Eoyce, " that a smaller picture should be 
a perfect representation of a larger object is a perfectly de- 
finable ideal." 105 But that, even as an ideal, it is not a self- 
contradictory conception is by no means clear. If only de- 
tails that are visible to the naked eye are pictured, there is no 
difficulty ; for a microscope may be used to read the map. But 
if the object to be pictured is itself viewed under the micro- 
scope, and all the details thus visible are to be represented, it 
is clear that if the map or picture were much smaller than the 
original, exact legible representation would be impossible. If 
now it be replied, as Eoyce would perhaps reply, that the 
quality of being legible is irrelevant to the notion of perfect 
mapping, that all that is meant by it is, that for every detail 
of the original there shall be a corresponding detail in the 
copy, then it is clear that, if both original and copy are as- 
sumed to be made up of a finite number of indivisible units, 
such perfect mapping is impossible, unless the copy be as- 
sumed to possess a finer texture than the original (i. e., to 
contain a greater number of indivisible units to the square 

104 World and Individual, I, 503 ff. 
io5Hiboert Journal, I, 27. 



Theology and the "New Infinite." 67 

inch). If, however, there is assumed to be no difference in 
texture, the points or ultimate units of which the material of 
the map or picture is composed must be infinitely numerous. 

In other words, the perfect representation of any object on 
a smaller scale implies, either that the copy, although smaller, 
contains exactly as many ultimate units as the original, or 
else that the copy is a continuum, or at least a compact collec- 
tion of points. If we assume the notion of the continuum, 
there is, then, no difficulty in the idea of a perfect represen- 
tation of a larger by a smaller surface. Indeed, if we assume 
that space is continuous or compact, such representation is an 
everywhere-present fact; because, for every point in a solid or 
a surface, there must then be assumed to be a point in any 
other solid or surface, however small the latter may be. 

It is clear, then, that the idea of an absolutely perfect repre- 
sentation, even without the added notion of ^/-representa- 
tion, requires the conception of an infinite multiplicity of ele- 
ments, unless we make the above-mentioned assumption con- 
cerning the finer texture of the material of the copy. It is 
indeed essential to Royce's argument that the map be drawn 
upon the soil of England, and therefore be an example of self- 
representation ; but this is not essential to the idea of the map 
as an illustration of infinity. All that is required is the as- 
sumption that for every point in the surface of England there 
shall be a point on the map, however small the map is drawn. 
But as I have already remarked, this follows from the notion 
of the continuum. If two surfaces are both assumed to be 
continuous, then, however large the one may be and however 
small the other, for every point in the one there is a point (or, 
for that matter, and this destroys the notion of a definite 
representation, there are two, three, or as many as you please) 
in the other. Instead, then, of supposing a map within a map, 
and so on forever, we can just as well suppose the original 
map without the loss of any detail to become smaller and 
smaller without limit. On either assumption the perfect map- 
ping, even of only the visible markings of England's surface, 



68 The Argument for a Finitist Theology. 

would imply the notion of an infinite multitude of points in 
any designated portion of the surface upon which the map is 
drawn. 

In the case of ^/-representation, or rather of representa- 
tion hy a part of that which is represented, it is obvious that 
the notion of infinite multitude must be assumed ; for here we 
have representation on a smaller scale, and there is no dif- 
ference in the texture of the original and the copy, or at least 
of part of the original and the copy. We find then that we 
have been traveling in a circle. In an effort to avoid the end- 
less regress we have defined a conception of self -representation, 
only to find, when we examine our conception a little more 
closely, that it contains the very notion which it was designed 
to escape. If, then, the notion of an endless regress is self- 
contradictory, that of self-representation, or of a purpose that 
is infinitely rich in implications, is likewise self-contradictory. 

We conclude, therefore, that the "discovery" of the so- 
called New Infinite leaves the problems of theology exactly as 
it found them ; and that the apparent bearing of the new con- 
ception of infinity upon these problems is the result of a! 
double use of such terms as "totality" and "equality." 106 

106 The reader may be interested in Koyce 's use of the New Infinite to 
explain the relation of the Absolute to the Particular Self (Hibbert Jour- 
nal, I, 44) and in Keyser's attempt by its aid to defend the doctrine of 
the Trinity and that of the divine omniscience (The New In-finite and the 
Old Theology, pp. 8off.). It seems clear that both writers are merely 
playing on the word equality. 

Professor Eoyce suggests that "a, wholly new light" is thrown "upon 
the possible relations of equality which, in a perfected state, might exist 
between what we now call an Individual or a Created Self and God as the 
Absolute Self. Perhaps a being, who, in one sense, appeared infinitely 
less than God, or who at all events was but one of an infinite number of 
parts within the divine whole, might, nevertheless, justly count it not rob- 
bery to be equal to God, if only this partial being by virtue of an im- 
mortal life or of a perfected process of self -attainment, received in the 
universe somewhere an infinite expression." "When we recall, however, 
that to be 'equal' here means no more than to be of the same "Mtichtig- 
Tceit," i. e., to be in the relation of one-to-one correspondence, it is far 
from clear that the "infinite expression" of the partial being is of any 
spiritual or ethical significance. 



Theology and the "New Infinite. 



69 



Professor Keyser, who is by profession a mathematician, tells us that 
it is a great error to suppose that the whole-part axiom is universally 
valid. It ought rather to be considered as a "logical blade" which 
divides the finite from the infinite. Some of the difficulties of theology, 
Professor Keyser assures us, have been caused by assuming that this 
axiom applies to infinites. 

Thus the doctrine of the Trinity has been pronounced absurd, because 
it implies that one infinite is composed of three infinites, and that each of 
the three is equal not only to each of the others but to the whole which 
they jointly constitute. But this objection, says Keyser, erroneously as- 
sumes that the whole-part axiom holds for infinites. He illustrates the 
logical possibility of the conception of a One which is also Three by 
means of the relation of the number-system to certain of its parts. Let 
M be the manifold of all rational numbers, E of the even numbers, 
of the odd numbers, and F of the rational fractions; then it is evident 
that E, 0, and F are proper parts of M; and also that a one-to-one corre- 
spondence is discoverable between M and each of these parts taken sep- 
arately. Therefore by Dedekind's definition, M, E, 0, and F are all in- 
finite manifolds. "What is important is now obvious," says Keyser. 
"It is that we have here three infinite manifolds, E, 0, F, no two of 
which have so much as a single element in common, and yet the three 
together constitute one manifold M exactly equal in wealth of elements 
to each of its infinite components." The application to the theological 
Trinity is of course evident. 

An obvious objection here presents itself. One might naturally inquire 
why there are just three rather than two or four persons. Indeed the 
mathematical analogy suggests an infinity, or at least a very large number, 
of constituent persons; and, as we have seen, Royce holds that the Abso- 
lute may be conceived without contradiction to include a multitude, and, 
in fact, an infinite multitude, of selves. This objection, however, misses 
Keyser 's point, which is, not that the doctrine of the Trinity can be 
mathematically demonstrated, but merely that, if on some other ground 
we believe that the One is Three and the Three are One, the conception is 
not logically absurd. 

It may be questioned, however, whether the aid thus so kindly prof- 
fered by Mathesis to Theology will be very enthusiastically received. On 
the one hand, Trinitarians like Cardinal Newman, who seems to have liked 
the doctrine all the more on account of its incomprehensibility (see New- 
man, The Grammar of Assent, pp. 124 ff.), may even be disposed to 
resent this attempt to make their cherished formula as plain and clear as 
the multiplication table or the rule of three; for, if the Trinity is not in- 
comprehensible, half the merit of assenting to the ancient creeds will be 
lost. On the other hand, adherents of the "new theology" who still con- 
sider themselves Trinitarians have learned to interpret the ancient for- 
mulae in such a way as to remove the contradiction; and therefore do not 
recognize the need of a demonstration of the conceivability of a numer- 
ical Trinity in Unity. 



70 The Argument for a Finitist Theology. 

The ' l new ' » conception of infinity is also employed by Professor Keyser 
in defense of the doctrine of the divine omniscience. Objection has fre- 
quently been made to this doctrine on the ground that it seems to abolish 
human freedom and to make God responsible for human sin. Keyser sug- 
gests that we may preserve the dignity of omniscience while giving up 
omniscience in the strict sense of the term. Suppose the knowledge of all 
events to include an infinite number of knowledge-elements. Now suppose 
this infinite manifold to be divided by a plane which in our imaginative 
construction represents the present instant. Then it is evident that there 
is a one-to-one correspondence between the manifold of elements either be- 
fore or behind this boundary and the undivided manifold. In other words, 
the knowledge of the past alone is just as infinite as the knowledge of 
the events of all time. Accordingly, even if God is assumed to have no 
knowledge of undetermined future events, His knowledge is nevertheless 
infinite; and, in the phraseology of the partisans of the New Infinite, 
God may still be said to possess the dignity or Machtigfceit of omnis- 
cience. The same argument is easily made to fit the case of omnipotence 
or of omnipresence. In an infinite world the Deity might then be infinite 
in knowledge, power, etc., without being omniscient, omnipotent, or omni- 
present. One may, however, be sufficiently lt tough-minded ' ■ to inquire 
just what is the value of the word ' ' infinite ' ' and the phrases 1 1 dignity of 
omniscience, ' ' etc.? Certainly no one would hold that merely to be in- 
finitely rich in numerical elements is a quality which is of any ethical 
value; for, if it were, then any portion of a continuum would possess this 
transcendent dignity. 



VII. 

Concluding Keflections on Einitist Theology. 

1. A Recapitulation of the Argument for the Divine Fin- 
itude. — We have been led to conclude that God is finite in both 
senses of the word — that he is not infinite either in the sense 
of including or possessing an infinite number of elements, or 
in the sense of including or controlling the whole of reality. 
Our position is therefore completely opposed to that of monis- 
tic idealism, according to which God or the Absolute is infinite 
in both these senses. It may be well to give a summary re- 
statement of the reasonings which have led us to this con- 
clusion. 

(a) As Koyee himself has shown, his conception of the 
Absolute presupposes the notion of the realized infinite. But 
the conception of a realized infinite is a contradiction in terms ; 
for that which is infinite or endless is not realized or complete. 
And the " new " conception of infinity does not escape the log- 
ical defect of the " old " ; for, as we have seen, the attempt to 
get rid of the self-contradiction by including it in the defini- 
tion is not satisfactory: the contradiction, though concealed 
from view, still remains. 107 

(b) The Absolute is said to experience all in an "Eternal 
Now " ; but the notion of an experience which is itself " time- 
less" while yet including experiences of temporal relation is 
self-contradictory. 108 Moreover the " Eternal Now " would be 
a realized infinite, and on that account, too, logically impos- 
sible. 109 

(c) The Absolute is an all-containing mind and possesses 

107 Chapter VI. 

108 Chapter II, Section 2 (6). 
loo Chapter VI, Section 2. 

71 



72 The Argument for a Finitist Theology. 

an all-inclusive experience. Now there can be no all-inclusive 
experience ; for it is psychologically impossible for certain of 
the experiences of the individual mind, especially such as are 
conditioned by limitation and isolation, to be identical parts 
of an all-inclusive mind. For such a mind, by virtue of the 
fact that it is all-inclusive, is unable to have these experiences. 
And yet if it does not have them, it is not all-inclusive. 110 

(d) The identification of God with the Absolute is vetoed 
by the ethical difficulty which besets every doctrine of the 
divine omnipotence. God is good; and, in a world such as 
ours, no good being can be omnipotent. Not only does this 
objection hold against the conception of the Absolute, but 
against that of a Mind that possesses a knowledge about all 
things without including everything as an identical part of 
its own experience; for, if a Being were omniscient even in 
this restricted sense, such a Being would be, if not in Royce's 
phrase "world possessing," yet certainly world-controlling, 
that is to say, omnipotent. 111 

(e) The theory of monistic idealism is unsatisfactory as a 
practical philosophy, inasmuch as it logically implies a life of 
acquiescence rather than of action. 112 

(/) Considered as the equivalent of or as a substitute for 
the traditional idea of God, the Absolute is religiously inade- 
quate. It lacks worth, and does not satisfy man's craving 
for fellowship with a Person. 11 * 

On the other hand, the theory of a Supreme Being who is 
limited in knowledge and power is logically unobjectionable, 
is not inconsistent with the presence of evil in the world as it 
now is, implies the genuineness of human cooperation with 
God in the contest with evil, and offers man an Object worthy 
of his worship, a Person who desires his love. 

3. The Difficulties of Finitist Theology. — Let us not, how- 
ever, assume too hastily that finitist theology is completely 

no Chapter II, Section 2 (6). 
in Chapters III and IV. 
H2 Chapter II, Section 2 (c). 
us Chapter II, Section 2 (a) . 



Concluding Reflections on Finitist Theology. 73 

satisfactory as a religious doctrine. Several questions present 
themselves : 

(a) Is Finitist Theology a Monotheism or a Polytheism? — 
If God is the whole of existence, or even if he is assumed to 
be distinct from, or only a part of, the universe but yet om- 
nipotent, there can be no doubt that there is but one God ; for 
there can not be more than one whole of existence or more 
than one omnipotent. If, however, we maintain that God is 
only a part of being, and that his power is so limited that some 
parts or aspects of being are not subject to his control, the 
proposition that there is but one God is far from self-evident. 

For most of us, indeed, the issue of polytheism versus 
monotheism does not present a " live option." It does not ap- 
pear to have been a live issue even for William James. 
Charles Kenouvier, however, declines to decide one way or 
the other, and, indeed, is very favorably disposed toward poly- 
theism. " The doctrine of unity," he says, " submits all the 
beings of the world to a royal authority which varies from the 
most absolute autocracy to a government tempered by a meas- 
ure of liberty conceded to the subjects." 114 On the other hand, 
the doctrine of a plurality of divine beings appears to Kenou- 
vier more accordant with republicanism. " Polytheism is the 
plurality of powers in the unity of direction." The same con- 
siderations which make for a belief in immortality lead Kenou- 
vier to look with favor upon the conception of a plurality of 
Gods. He thinks it improbable that all personal beings but 
one should be such as to be included in the class of men ; and, 
like the ancients, supposes that men may be raised to the rank 
of Gods. 115 

One of his interpreters remarks that, though one may at 
first be surprised and possibly shocked by Renouvier's evident 
liking for polytheism, the saint-worship of the Roman Cath- 
olic Church would readily suggest such a doctrine. Further- 
more, "the theology of the Councils of Nicaea, of Constanti- 

11* Kenouvier, Psychologie rationelle, Vol. Ill, p. 259. 
"5 Ibid., pp. 255 f. 



74 The Argument for a Finitist Theology. 

nople, of Chalcedon, affirm, and modern theologians still ac- 
cept, the multiplicity of divine persons. The Christian Trin- 
ity is not a doctrine of the divine unity." 116 

It is true that Renouvier suggests that "this polytheism is 
far from being irreconcilable with the unity of God; . . . 
for the one God would then be the first of the superhuman 
persons, rex hominum et deorum." 1 17 It is, however, perfectly 
conceivable that there should be a number of superhuman per- 
sons all finite in power, and that none of them should be 
"king." Indeed, to anticipate the theoretical doubt which is 
discussed in the next section, if all the members of such a 
pantheon, whether it were monarchical or democratic in its 
organization, could be known to be good, it is not evident that 
the polytheistic conception would be religiously unsatisfying. 
However, as remarked above, the issue does not present a " live 
option," and it will be better to assume, in the further discus- 
sion, that there is but one God. 

(b) Is the Supreme Being Good? — It is true that the log- 
ical motive for the doctrine that God is finite is the desire to 
save his goodness. Our argument has been, God is good; the 
world is, in part, evil ; therefore God's power is limited. His 
finitude is thus an inference from his perfect goodness ; but it 
is evident that the argument cannot be reversed. The perfect 
goodness cannot be inferred from the finitude of the Deity. 

If we divest ourselves of our prejudices, and forget the 
affinity of the words good and God, it is possible to conceive 
the existence of a being who is immeasurably more powerful 
than all others, and yet is not good. Such a Supreme Being 
might be defined as Power plus Intelligence plus Conscious 
Purpose. But the purpose toward which the power is directed 
need not include any concern for the pains and pleasures or 
the ideal values of humankind. As a man intent upon the ac- 
complishment of some end goes his way, and does not even 
notice the ant-hill which his hurrying foot has demolished, so 

lie Arnal, Philosophie Beligeuse de Charles Benouvier, pp. 148 f . 
ii7 Psychologie rationelle, III, 255. 




Concluding Reflections on Finitist Theology. 75 

the Supreme Purpose might seek its own fulfilment wholly 
regardless of the hopes and wishes of the denizens of our 
planet. A consciously purposive Power wholly uninterested 
in the aifairs of men is, accordingly, a logically possible con- 
ception of God. 

Even the addition to this conception of that notion of an 
interest in human doings and sufferings which, I have said, is 
not necessarily included in the universal purpose, does not 
bring us at once to the Christian thought of a Father-God. It 
may indeed fall far short of it. The interest of the Supreme 
Power in human affairs might be entirely non-moral. It might 
be an interest in mundane happenings as a spectacle. Such 
a God might take pleasure in the happiness of his creatures, 
and also in their pains and disappointments, in their sorrows 
as well as in their joys. In short God as thus defined might 
be a Supreme Setebos, like him of whom Caliban muses in 
Browning's verse: 

Thinketh such shows nor right nor wrong in Him 
Nor kind, nor cruel: He is strong and Lord. 
'Am strong myself compared to yonder crabs 
That march now from the mountain to the sea; 
'Let twenty pass, and stone the twenty-first, 
Loving not, hating not, just choosing so. 

If, now, we add to our conception of a Supreme Being the 
notion of moral quality, there still remains a horrible and 
repulsive possibility ; for moral quality may be bad as well as 
good. The Supreme Power might be malevolent. 

A reversal of the traditional theodicy is not inconceivable. 
Indeed the very argument by which men have sought to prove 
that this is the best might be employed with a few alterations 
to prove that it is the worst possible world. The elements of 
goodness which mar the perfection of absolute evil might be 
said to be required to set off the evil by contrast; or the 
Supreme Fiend might be supposed to be limited in his man- 
agement of the universe by a sort of " iron law of wages " : a 
certain amount of pleasure might be necessary to insure the 
continuance of the pain-economy. 



76 The Argument for a Finitist Theology. 

To be sure, no one takes such a possibility very seriously; 
yet, from the standpoint of mere logic and cold facts, it is not 
unthinkable. The goodness of God cannot be proved. It can 
only be believed; that is, assumed as a working principle of 
human life. And, unless this assumption is made, the doc- 
trine of a finite God has no religious value. 

(c) Does the God of Finitist Theology Exist? — In a dis- 
cussion of the adequacy of the idea of God the existential 
question can not be wholly ignored. It is true that the value of 
the idea is not wholly dependent upon its objective reality; 118 
yet, if a man were convinced that the idea of God is merely 
an ideal, then for him its value would be seriously impaired. 
If the existence of God is to be proved, the demonstration will 
have to consist in an exhibition of the evidences of his pres- 
ence in the world. But no one will maintain that the argu- 
ment from design establishes more than the probability of 
God's existence. Moreover, if, without evidence of his 
presence, we could become convinced of his existence, mere 
existence would not be enough. An entity that does nothing 
(although the thought of such an entity might avail to relieve 
one's loneliness) would not be completely adequate. From this 
point of view the question of the existence of God merges in 
that of his power. 

We have criticized monistic idealism on the ground that, 
by reason of its doctrine of the eternal perfection of the 
Whole, it tends to quietism, to the mood of the "moral hol- 
iday." But there is danger of reaching a similar position 
from the opposite direction. The finite God may be so limited 
in our thought of him as to make it doubtful whether he can 
in any significant sense be said to be supreme. Thus the same 
modification that makes the traditional doctrine of God the- 
oretically tolerable threatens to destroy its practical value. 
For if men should be convinced that, while there is a God, 
his power and intelligence are not adequate to the task of 
world redemption, they would fall into despair; and nothing 

us Mill, Autobiography; Vaihinger, Die Philosophie des als Ob. 



including Reflections on Finitist Theology, 77 

so completely paralyzes action as despair. There is inspiration 
for strong natures in the thought of cooperation with a God 
who actually needs our help ; but not all are strong, and even 
the strongest and most daring spirits have their hours of de- 
pression, when they need to feel that there is sufficient power 
on their side to assure the ultimate victory of the Eight. From 
this point of view the question of God's existence is equivalent 
to a question about the salvability of the world. It may, ac- 
cordingly, be rephrased thus: Is there, in this world of ours, 
sufficient power and intelligence in the service of good will, to 
assure the realization and preservation of the values that we 
hold dear? 

4. Finitist Theology and the Right to Believe. — By Wil- 
liam James finitist theology is combined with a doctrine of 
the " will to believe." The existence of God can not be proved 
by scientific methods of demonstration. Considered ;as a 
hypothesis it is, indeed, not inconsistent with the facts; but 
neither is the contrary hypothesis. Now, says James, this is 
a case where we ought to practise the will to believe. " Our 
passional nature not only lawfully may, but must, decide an 
option between propositions, whenever it is a genuine option 
that cannot by its nature be decided on intellectual grounds." 119 
In other words, though James nowhere puts it in just this 
way, we are at liberty to act as if we were certain of God's' 
existence, even if we have no intellectual grounds, or have only 
insufficient grounds, for certainty. 

There are, however, obvious objections to this procedure. 
It seems to encourage the all too common tendency to super- 
ficial thinking, where one's own interests and prejudices are 
involved; and there appears to be a suggestion of intellectual 
dishonesty in the proposal to believe when there is not sufficient 
evidence to convince the reason. In my opinion, however, 
these objections are based upon a failure to distinguish be- 
tween different senses of the word " believe." It must be ad- 
no The Will to Believe, p. 27. 



78 The Argument for a Finitist Theology. 

mitted, I fear, that James himself is partly responsible for 
these confusions. 

There are at least three kinds of " believing." In the first 
place, one may be said to believe when he feels that he knows. 
Secondly, belief may be understood in a wholly practical 
sense. One shows his faith by his works; and it is easy to 
pass from this principle to the view that faith, or belief, is 
the action which would normally accompany or result from 
belief in the first sense. It is this second sense of believing, 
the acting as if one knew, which James seems to have chiefly 
in mind when he speaks of a " will to believe." 

There is, however, a third sense of the word "believe," 
which seems to be implied, though not clearly distinguished 
from the others, in James's exposition. It differs from our 
first sense in being without real or supposed theoretical jus- 
tification; and from the second in being an affair of feeling, 
rather than of will or action. If the first kind of believing 
is the "feeling that one knows," and the second, "the acting 
as if one hnew," the third may be said to be "the feeling as 
if one hnew." 

That this third kind of belief is psychologically possible 
is a matter of everyday experience. Our feelings are seldom 
quite appropriate to the theoretical situation. The passenger 
on the railway train who is nervous and ill at ease because of 
the fear of a wreck is permitting emotion to outrun the evi- 
dence. But the same is true of the passenger who has no 
feeling of anxiety whatever; for there is some danger. And, 
while the probability of a wreck is not sufficiently great to 
justify the fears of the one, it is not so small as to justify the 
utter calm of the other. Belief, in the third sense, the feeling 
as one would feel if one had theoretical knowledge which he 
does not have, is thus illustrated by our usual freedom from 
emotional disturbance on a rapidly moving train. We know 
that a thousand and one things might happen, any one of 
which might plunge us to almost instant death; we may be 
theoretically persuaded that there are a given number of 



Concluding Reflections on Finitist Theology. 79 

chances in ten million that we will on this particular day be 
killed in a wreck ; we may even allow our minds to dwell upon 
these chances of destruction ; and yet feel as we should feel if 
the chance were absolutely nil. 

This sort of belief is even better illustrated in our social 
relations. Here, too, the degree of certainty which we feel is 
not usually the exact degree that would be logically appro- 
priate to the situation. We cannot prove that the bank will 
not fail; that people are telling us the truth; that our best 
friends will not play us false ; that the Causes to which we de- 
vote ourselves are really worthy of our devotion. We can have 
no intellectual certainty in regard to these matters; and yet 
we not only act but also feel as we should act and feel if we 
were intellectually certain. In a word, our faiths and loyal- 
ties habitually outrun the evidence. 

In the same way, although we do not know that there is a 
God, or that the world is moving toward a worthy goal, and 
cannot therefore be said to believe in the existence of God or 
in the salvability of the world in the first of our three senses 
of the word " believe," we have the right to believe in the other 
two senses. We are justified in accepting the existence of 
God as an assumption in accordance with which to plan our 
lives; and also in feeling a greater degree of certainty with 
reference to his existence than is theoretically warranted. 



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80 



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McTaggart. Studies in Hegelian Cosmology. Cambridge, 1901. 

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82 The Argument for a Finitist Theology. 

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VITA. 

Kay Harbaugh Dotterer was born in Westmoreland County, 
Pennsylvania, Aug. 4, 1880. He attended the public schools, 
and taught two terms. In 1902, he was graduated at the Cen- 
tral State Normal School, Lock Haven, Pa.; in 1906, at 
Franklin and Marshall College; in 1909, at the Theological 
Seminary of the Reformed Church, Lancaster, Pa. Prom 
June, 1909, to January, 1913, he was pastor of a Reformed 
Church at Rockwood, Pa., and from 1913 to the present, in 
Baltimore, Md. In 1910, he completed a graduate course, and 
received the degree of Ph.M. from Franklin and Marshall Col- 
lege. Since October, 1913, he has been a student in the Johns 
Hopkins University. His subjects have been Philosophy, 
Psychology, and Education. In 1916 he received the degree 
of Master of Arts, having submitted an essay on " The Philos- 
ophy of the ' As If ' in its Application to Theology." 



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